{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 " Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 } } {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "x,y:=1,0;to 8 do c := simpli fy(1/sqrt(x**2+y**2));\n x,y:=op(simplify([x-c*y,y+c*x])) od:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>6$%\"xG%\"yG6$\"\"\"\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "t:=n->if n=0 then 0 else sum (arctan(1/sqrt(k)),k=1..n) fi;r:=n->sqrt(n+1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"tGf*6#%\"nG6\"6$%)operatorG%&arrowGF(@%/9$\"\"!F/-% $sumG6$-%'arctanG6#*&\"\"\"F7-%%sqrtG6#%\"kG!\"\"/F;;F7F.F(F(F(" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rGf*6#%\"nG6\"6$%)operatorG%&arrow GF(-%%sqrtG6#,&9$\"\"\"F1F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 166 "N:=16:display(plot([seq([[0,0],[r(n),t(n)]],n=0..N)] ,coords=polar,color=black),\nplot([seq([r(n),t(n)],n=0..N)],coords=pol ar,color=red),scaling=constrained,axes=none);" }}{PARA 13 "" 1 "" {GLPLOT2D 406 374 374 {PLOTDATA 2 "67-%'CURVESG6$XH%)anythingG6\"6\"[g l'!%\"!!#%\"#\"#!!!!!!!!!!!!!!!!!!!!!!!!!!!!00000000000000000000000000 0000003FF00000000000000000000000000000-%'COLOURG6&%$RGBG$\"\"!F/F.F.-F $6$XHF'F(F)[gl'!%\"!!#%\"#\"#!!!!!!!!!!!!!!!!!!!!!!!!!!!!0000000000000 00000000000000000003FEFFFFFFFCDA5823FEFFFFFFFE9D5F3F*-F$6$XHF'F(F)[gl' !%\"!!#%\"#\"#!!!!!!!!!!!!!!!!!!!!!!!!!!!!0000000000000000000000000000 00003FD2BEC3333567733FFB504F335B7388F*-F$6$XHF'F(F)[gl'!%\"!!#%\"#\"#! !!!!!!!!!!!!!!!!!!!!!!!!!!!00000000000000000000000000000000BFE62AA4646 B9C913FFE04F379F4C7D8F*-F$6$XHF'F(F)[gl'!%\"!!#%\"#\"#!!!!!!!!!!!!!!!! !!!!!!!!!!!!00000000000000000000000000000000BFFA17CBEF1710093FF87A4A60 C27851F*-F$6$XHF'F(F)[gl'!%\"!!#%\"#\"#!!!!!!!!!!!!!!!!!!!!!!!!!!!!000 00000000000000000000000000000C00285155E55B08D3FE99DFD46BEAA26F*-F$6$XH F'F(F)[gl'!%\"!!#%\"#\"#!!!!!!!!!!!!!!!!!!!!!!!!!!!!000000000000000000 00000000000000C0052267CBFC42E3BFC280AB8E092EA4F*-F$6$XHF'F(F)[gl'!%\"! !#%\"#\"#!!!!!!!!!!!!!!!!!!!!!!!!!!!!00000000000000000000000000000000C 004B2831BA136E0BFF249F742AAA7F0F*-F$6$XHF'F(F)[gl'!%\"!!#%\"#\"#!!!!!! !!!!!!!!!!!!!!!!!!!!!!00000000000000000000000000000000C00176D9855A1D04 C000764A3463BBA8F*-F$6$XHF'F(F)[gl'!%\"!!#%\"#\"#!!!!!!!!!!!!!!!!!!!!! !!!!!!!00000000000000000000000000000000BFF7F42C3D62D975C0064892B612F02 2F*-F$6$XHF'F(F)[gl'!%\"!!#%\"#\"#!!!!!!!!!!!!!!!!!!!!!!!!!!!!00000000 000000000000000000000000BFE3B891690FE4EAC00A12279D590C19F*-F$6$XHF'F(F )[gl'!%\"!!#%\"#\"#!!!!!!!!!!!!!!!!!!!!!!!!!!!!00000000000000000000000 0000000003FD77187ED6E0825C00B8EB472F617ACF*-F$6$XHF'F(F)[gl'!%\"!!#%\" #\"#!!!!!!!!!!!!!!!!!!!!!!!!!!!!000000000000000000000000000000003FF5C5 6B22678F7AC00AB624AE329015F*-F$6$XHF'F(F)[gl'!%\"!!#%\"#\"#!!!!!!!!!!! !!!!!!!!!!!!!!!!!0000000000000000000000000000000040024B44DA741B12C007B 13FCBA40967F*-F$6$XHF'F(F)[gl'!%\"!!#%\"#\"#!!!!!!!!!!!!!!!!!!!!!!!!!! !!000000000000000000000000000000004008A04665E15622C002CD97C9BA903CF*-F $6$XHF'F(F)[gl'!%\"!!#%\"#\"#!!!!!!!!!!!!!!!!!!!!!!!!!!!!0000000000000 0000000000000000000400D7B23ABCBBB3BBFF8E3AC17DB76B0F*-F$6$XHF'F(F)[gl' !%\"!!#%\"#\"#!!!!!!!!!!!!!!!!!!!!!!!!!!!!0000000000000000000000000000 000040104BCC9768B0A7BFE44C34843A5091F*-F$6$XHF'F(F)[gl'!%\"!!#C\"2\"#! !!!!!!!!!!!!!!!!!!!!!!!!!!!3FF000000000000000000000000000003FEFFFFFFFC DA5823FEFFFFFFFE9D5F33FD2BEC3333567733FFB504F335B7388BFE62AA4646B9C913 FFE04F379F4C7D8BFFA17CBEF1710093FF87A4A60C27851C00285155E55B08D3FE99DF D46BEAA26C0052267CBFC42E3BFC280AB8E092EA4C004B2831BA136E0BFF249F742AAA 7F0C00176D9855A1D04C000764A3463BBA8BFF7F42C3D62D975C0064892B612F022BFE 3B891690FE4EAC00A12279D590C193FD77187ED6E0825C00B8EB472F617AC3FF5C56B2 2678F7AC00AB624AE32901540024B44DA741B12C007B13FCBA409674008A04665E1562 2C002CD97C9BA903C400D7B23ABCBBB3BBFF8E3AC17DB76B040104BCC9768B0A7BFE44 C34843A5091-F+6&F-$\"*++++\"!\")F.F.-%*AXESSTYLEG6#%%NONEG-%(SCALINGG6 #%,CONSTRAINEDG-%%VIEWG6$%(DEFAULTGF]p" 1 2 0 1 10 0 2 9 1 1 1 1.000000 43.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve \+ 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Curve 12" "Curve 13" "Curve 14" "Curve 15" "Curve 16" "Curve 17 " "Curve 18" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "N:=150:dis play(plot([seq([r(n),t(n)],n=0..N)],coords=polar,color=red),scaling=co nstrained,axes=none);" }}{PARA 13 "" 1 "" {GLPLOT2D 414 390 390 {PLOTDATA 2 "6&-%'CURVESG6$XH%)anythingG6\"6\"[gl'!%\"!!#i]l\"bt\"#!!! !!!!!!!!!!!!!!!!!!!!!!!!!3FF000000000000000000000000000003FEFFFFFFFCDA 5823FEFFFFFFFE9D5F33FD2BEC3333567733FFB504F335B7388BFE62AA4646B9C913FF E04F379F4C7D8BFFA17CBEF1710093FF87A4A60C27851C00285155E55B08D3FE99DFD4 6BEAA26C0052267CBFC42E3BFC280AB8E092EA4C004B2831BA136E0BFF249F742AAA7F 0C00176D9855A1D04C000764A3463BBA8BFF7F42C3D62D975C0064892B612F022BFE3B 891690FE4EAC00A12279D590C193FD77187ED6E0825C00B8EB472F617AC3FF5C56B226 78F7AC00AB624AE32901540024B44DA741B12C007B13FCBA409674008A04665E15622C 002CD97C9BA903C400D7B23ABCBBB3BBFF8E3AC17DB76B040104BCC9768B0A7BFE44C3 4843A50914010E955110DD0733FD6A48C69EEED61401093F0E9E80A373FF59ADEE9B8D 854400EAD729FA92465400268B067EF33EB400A8FA88F5D8207400944C5FCB2CCDF400 50C0E6D6FF38C400F10949C02595F3FFCD91EF9766E7F4011C6A8B38D202A3FEC0B37D 250E558401347A2919FD063BFBB851F29CA01024013FED106511090BFF1B75F917D4CE 84013E8CCED66CE86C000AAD0F7F507B340130A6F7EC01A78C007FEFCC60E6AB240116 FDC6651B91FC00E962B1173E5C4400E56CE6F2C78A0C0121C36C7C4BB974008A8C7D88 EF138C0145C7D47F2B44E40020BDFE9E5B490C015FB5DCA7ED01A3FF576FC8375506BC 016EE367735ECC63FD7AF598D1BEFB2C017302E5D789351BFE4174EE0799E99C016C1E C1F7F377CBFF9F3D7384BB650C015A92B398F4AFCC004AB710A600CCCC013F0372245C A72C00BE3D4CB45F0CFC011A5532C3558F5C011390B1D0BF9B3C00DB42AC7FB415DC01 415D9ADFAE27CC007457509435965C01676ABC144AD0BC0002AEF6FA2AF78C0184DA63 6982286BFF1273CB2D9F0B2C01990D8878FB1CDBFB5FABAF0C8E525C01A3A3DD0CCAE6 13FED3FF4E8F5A9AEC01A47A6168B22EC3FFE78E739251E26C019BA8AD34AB1D24006E 82DD9D15D74C01897D1DDE53C2B400E28B70FC48D59C016E781BBAC4B8940126BA34F0 80964C014B46A6DC2D4AF401568AFE1F4959CC0120BC5A35B34634017FCA78CD40E51C 00DF9A2263FEA3D401A1B4326CAF4B5C00730CB46C2A20F401BBAEBC74A02F2BFFFC23 6785E02C3401CD4C911ECC1C0BFF0607092C33AD8401D64C120842BEEBFA123FAE851A 381401D696B621F9C603FEEEDAA9516864D401CE3F79C6A97C93FFF53E6653CCBF9401 BD80A8BA503CC4007629AF4AC127B401A4B918D775ED1400EC2DE9BAF70D94018468ED C4475824012D55541FB41164015D2DFBB95BA124015FE664AA710CD4012FBFE15C5BED 14018CFA97156BC2D400F9D7DB6096892401B3DEB90A59BDE4008B21D1587A5F6401D3 FDB7C12CCF640015359D5EC2201401ECE1CF2FCDFD13FF33FA53C11A045401FE3528FF 8969A3FCB6C0681295E5540203E0FA7D6C5F9BFE922251AD9B17240204B9013B31DCEB FFC7E2C27F880B740201A6F2ED0BABFC0060EC2B3BA0132401F57BB462431A4C00D9AA 5E4AFD79B401E03D625A16962C01263B7D5D3F590401C3EECF988169DC015BDDEFF411 0AD401A1038EBC432DCC018D03336F297B44017804732EE2204C01B905A2590320E401 498CF32273DBCC01DF54DC56862204011648669FC624FC01FF76FE5AC2DE4400BDDE67 8464A8DC020C84C1387967E4004887DB1EAFAB0C0215E0E2C099ACB3FF9C41D2C21DA2 8C021BB69C8522C563FE4118FD91A1E4BC021DF8A1DCC472ABFD7B40A4C1C44EDC021C A56B2800307BFF5E97F320073D1C0217C6DD1E4DD2FC002DCE61FD73E47C020F71D029 C2A7FC00A96411FF46A03C0203C57AACFB37AC01104907F5F82CFC01E9D584161A726C 0148F8D7F75FC6AC01C626EABFD535EC017E1A1D14548C3C019CF2EB1BB96BCC01AF13 1105C6160C016EBB9D19008D3C01DB58E52BEFADAC013C0F88A92A536C0201387605A7 12AC010587B0231F29BC0211F8C383DE0C1C00978B1EEBC95C5C021FC16D6D31E93C00 1EE22E1D00F60C022A6FA550FA53DBFF44DAA64BA913FC0231E9DD6C78551BFD1C51FA A0FF37FC02361FCF811FB9D3FE71A14066404ADC02370A69E85E5273FFB81C9B840E79 2C0234ABA45F2C0984005A11F016E79C1C022F0E3E3BBE494400D52711F76F5D4C0226 4567C0C23EA40126072E48B5CB9C021A6C584A2198F4015ECC18C68F5C8C020BA5D366 B01AC4019453A95F08DAEC01F4373DFCAEBC6401C619A2645B73BC01CBFBD85312A544 01F3A5336678A24C019F056A69103974020E44EFA07D594C016DCA25FD66DCA4022034 1EC026312C0138C914E62ACDB4022F7749594D3D4C010088AD13C2ECF4023BECA22681 474C008B2ABABB62C4C4024579937DBEDF0C0011002B7F708CC4024C0AD2FB8D36EBFF 27735CD9784F54024F9464B36AF16BFC4828130F9F88C40250118C1D7623C3FEADE6B0 49CC87F4024D84AD3E88A983FFD622E39E0B28E40247F71E478CB4C40069204E767C91 F4023F78EAC573FE2400E48924C4E9FAF402342089A0256BC4012E1C4A6AD14A940226 0A87499A910401679395CC0E267402155924075273F4019E2DB6EDE15364020233EA6F A97F3401D175D45D92C13401D98E76B72FBCC402007FE7C99A304401AA87A9B1802064 0216347EA6D7C7440177BCA383885AA40229AC63BA8D3A8401419D4B73F84584023AC0 99BDCA78A401089F2B62523F5402494FA758020CB4009A78B8ED598AA402553DC064EA C224001FE4E4EE7A77B4025E74E21743ED13FF45059BA7B1B5D40264E4E2A8DB2333FD 1AA8A97FAABCF4026883741691CB7BFE72845AB347FF6402694C1BD7B78BABFFB8BBF7 13497C940267401E659F16CC005AE3596D10413402626660071C076C00D73844A3DD85 E4025ACB3B97A3725C0128357D28FED6A40250804F6F86E92C0162C949FFCA74740243 9C41558F0CCC019AE84E06C7B36402343A7AC7E47E2C01D02944BEF744A402227ADD2A 45278C020114C552982E94020E817034993CBC021846DC876C5ED401F0EC142D67669C 022D81179979799401C107E622F4E1DC02409DC509F9E544018DB3097B6686FC02517B 84F001D65401574F8BEFE5390C025FFD72349876B4011E4409AE245F3C026C0B42B8D0 197400C5F5BD78EB506C0275915EE1B9D894004BC2A6AF23974C027C80EF66C3B6C3FF 9D9B2F99D995FC0280CFE290619713FE3FDFCB6E4A21FC028278E92170873BFD7EDF5B 6FF7687C02817B6AAF498A3BFF5F987473BCE15C027DDB71F937496C002EF94F6CCDC5 2C0277A192008AE64C00AC8719A38B77DC026EDAC357CC16BC0113CF46E664B94C0263 983B9E1A61EC014FB77E7DDDB64-%'COLOURG6&%$RGBG$\"*++++\"!\")$\"\"!F2F1- %*AXESSTYLEG6#%%NONEG-%(SCALINGG6#%,CONSTRAINEDG-%%VIEWG6$%(DEFAULTGF> " 1 2 0 1 10 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" }} }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 181 "N:=55:display(polarplot(t /2+1.0788914983295,t=-2*1.0788914983295..4*Pi,color=blue),plot([seq([r (n),t(n)],n=0..N)],coords=polar,color=red,thickness=2),scaling=constra ined,axes=none);" }}{PARA 13 "" 1 "" {GLPLOT2D 431 472 472 {PLOTDATA 2 "6'-%'CURVESG6$7dw7$$!0#*[u\"3&\\#=!#C$!0'Q'G-hMu#F*7$$!0VUcRR\"))=! #;$!0GK7`H*yLF07$$!0@vbq)o(4$F0$!02S()zZAa'F07$$!0-!4bf$3&RF0$!0hKm(QR H5!#:7$$!0@xG:$=YUF0$!0u%y\"p==U\"F=7$$!0%)3RC9I'RF0$!0'**GE%)o?=F=7$$ !0w;9>Xz<$F0$!0,,h-/A>#F=7$$!0M!GE0kK=F0$!0\\_/wnGd#F=7$$\"0$4(GjY@D\" !#<$!0BQ_$e3cHF=7$$\"0pbmp@0k#F0$!0,Fix\\6K$F=7$$\"0xT,kPF=7$$\"0EpMbV\\A)F= $!0uUh,[5K$F=7$$\"08Hk)G\"H$))F=$!0C%\\OTB&y#F=7$$\"0g1'fkOL$*F=$!04'z 'HtsD#F=7$$\"01*\\S)zs$)*F=$!0:x3\\eYi\"F=7$$\"050^y46.\"!#9$!0$)*4^W% z0*F07$$\"04vq4*=s5Fdt$!0g,:'eC<9F07$$\"0()R38kj5\"Fdt$\"00=P#4')4lF07 $$\"0t%*\\0;s8\"Fdt$\"080$[vc(e\"F=7$$\"0\"yX2,,e6Fdt$\"0?ly\")*fuCF=7 $$\"0e7q0@C<\"Fdt$\"0[V\"e,6jMF=7$$\"0`]Sb.\"y6Fdt$\"0]9lFD,R%F=7$$\"0 ak&=/(e<\"Fdt$\"0$=1Wv(3V&F=7$$\"0V?6%QPl6Fdt$\"0ld`;z%HkF=7$$\"0r'e]$ *RX6Fdt$\"0q\"\\>Q(e[(F=7$$\"0d!\\*eUn6\"Fdt$\"0!z7&>0N_)F=7$$\"0(e'41 \"*o2\"Fdt$\"0/d\"fJP1'*F=7$$\"0#z(f9\"))G5Fdt$\"0JHqGaP1\"Fdt7$$\"0r+ IVT)*p*F=$\"0i+R,Jr;\"Fdt7$$\"0`&p#4h$=!*F=$\"0^@nN&pm7Fdt7$$\"01StR=x I)F=$\"0_S%\\u#[N\"Fdt7$$\"0=IcNweR(F=$\"0(e#[\"\\(4X\"Fdt7$$\"0\\(fq_ w%\\'F=$\"0^xtpu<`\"Fdt7$$\"0c0VU)\\[aF=$\"0vOV`$o6;Fdt7$$\"0n!Rd\\ToV F=$\"06W/gr8o\"Fdt7$$\"0M$=%\\KX3$F=$\"0mOxt&3]F=$\" 0Gm03E:!=Fdt7$$\"0-,b4gc+&F0$\"0(\\gTx3]=Fdt7$$!02)o)o_yO)F0$\"07pcp=Y )=Fdt7$$!0^][/+GN#F=$\"0O$=]*36\">Fdt7$$!0G`GMM$)p$F=$\"0iDy**=S#>Fdt7 $$!03Z0!4?k_F=$\"0%GF^g,F>Fdt7$$!0SJA')\\8!oF=$\"0P4M#Rm<>Fdt7$$!0+o3o y=N)F=$\"0`@h<`f*=Fdt7$$!0aNZ!y0,**F=$\"0$eBtExh=Fdt7$$!0sX@.%RQ6Fdt$ \"0O#[5V(p\"=Fdt7$$!0Urv0@qH\"Fdt$\"0D(4=XEbX.Nyf\"Fdt$\"0W#\\Izr%f\"Fdt7$$!07Q9)))>J7$*yQ\"Fdt7$$!0@/B6[2+#Fdt$\"0f5\"GV%f E\"Fdt7$$!0@`&eHw?@Fdt$\"0tH^\\tG8\"Fdt7$$!0TP]0&eOAFdt$\"09=LapE#)*F= 7$$!0C(*=9=PL#Fdt$\"0!*>Mn+kL)F=7$$!0X!QI_$GU#Fdt$\"0'[\"z42Bs'F=7$$!0 z*oZa13DFdt$\"0?Z,BI3%[F=7$$!04@l6tCd#Fdt$\"07@F()oh0$F=7$$!0URB*)G]i# Fdt$\"0y$Gvdqg6F=7$$!0\"zmy7'Rm#Fdt$!0b0Y3UaH)F07$$!09n3t#G'o#Fdt$!0!* =3*f10FF=7$$!0@>8?n`p#Fdt$!0I))o!)zAu%F=7$$!0x9\"eb%*)o#Fdt$!0a/8#QZ\" z'F=7$$!0ME@ceYm#Fdt$!0wEiNs.+*F=7$$!0!3R9x-GEFdt$!0#\\\"\\K^_4\"Fdt7$ $!0jbDKwyc#Fdt$!0'4YgdR>8Fdt7$$!02s5l$3(\\#Fdt$!0)>*ekl$>:Fdt7$$!0moBp g;T#Fdt$!0!yjGw$Qr\"Fdt7$$!0s)=`\"*)GI#Fdt$!0h`n(y$y\">Fdt7$$!0$RZ\"pA j<#Fdt$!0Fuwsze6#Fdt7$$!0SR>.+k/#Fdt$!0k#oK;#*)G#Fdt7$$!02.7x$[$*=Fdt$ !07h6KnRY#Fdt7$$!01!4()z&*H!p' \\IFdt7$$!0x4TH\"*RC*F=$!0$yn*3!RgJFdt7$$!0kU#3_y**pF=$!0/Ds=[ZD$Fdt7$ $!0dO!ed.lYF=$!0CX#f%oIL$Fdt7$$!0#ecBSR/AF=$!0>58J 4*f.Z$Fdt7$$\"0)Q?'p\"f7#)F=$!0ijGQ-bX$Fdt7$$\"0S%*ou&o#4\"Fdt$!09\\Z' >R>MFdt7$$\"0B#HMimN8Fdt$!0&*)=ZcpoLFdt7$$\"0B]`Q^4i\"Fdt$!0cu-xthG$Fd t7$$\"0*)GDj@h&=Fdt$!0^!*\\]P%)>$Fdt7$$\"0#[%*4)[`7#Fdt$!0LiT;,W2$Fdt7 $$\"0VN)oytuBFdt$!0wGg*))zMHFdt7$$\"0%)fya#y*e#Fdt$!0JhIm/Iz#Fdt7$$\"0 6_h&\\]@GFdt$!0qi#G/v9EFdt7$$\"0\\pYe^B/$Fdt$!0X$G:Q#fT#Fdt7$$\"0u#Fdt7$$\"0\"RCmWADMFdt$!0O=(etT$)>Fdt7$$\"0fDo#yF$f$F dt$!0g=1/[Zu\"Fdt7$$\"0+%Q4([%\\PFdt$!00^4IvJ[\"Fdt7$$\"04;wFBg)QFdt$! 0[H9)f\")37Fdt7$$\"0_3$=RQ0SFdt$!0H$QJt$*Q\"*F=7$$\"0*4dG-'=4%Fdt$!09h TK%RZkF=7$$\"0fxLb!QnTFdt$!013]8#eFLF=7$$\"0*\\+2o3>UFdt$!0\"R>jC_l6F0 7$$\"0UD)GALXUFdt$\"0hKOYmY.$F=7$$\"0Su'=(R'[UFdt$\"0!\\J\\duHfF=7$$\" 0IH^^$pEUFdt$\"0Ktc)*eXR*F=7$$\"05?aA^e=%Fdt$\"0DT&HdCL7Fdt7$$\"0&>_gH ]7TFdt$\"0\"y,W!3Ld\"Fdt7$$\"06^nX'QCSFdt$\"0u!)**fu5(=Fdt7$$\"0pwBX'z -RFdt$\"0\"R*Rb0B>#Fdt7$$\"0%=ag^1jPFdt$\"0]km7C5\\#Fdt7$$\"0c-UZw11$Fdt7$$\"0q$\\d*)*3?$Fd t$\"0Rc@ZvjL$Fdt7$$\"0')QMhA\\&HFdt$\"0f[\\!3#og$Fdt7$$\"0#*R'HL:AFFdt $\"0Fyd4yu#QFdt7$$\"0jLYiMBX#Fdt$\"0q)*>Y7)[SFdt7$$\"0v(G3eya@Fdt$\"0X 8MyntD%Fdt7$$\"0gOq[Om%=Fdt$\"0-Vht:,W%Fdt7$$\"0FPXK#)Q`\"Fdt$\"0!pp9F e&f%Fdt7$$\"0#e3qcir6Fdt$\"0v3&>b=UZFdt7$$\"0bR4-**QM)F=$\"0y3F*zU\\[F dt7$$\"0350*Q0SYF=$\"0#e:&>us$\\Fdt7$$\"0^PwOg\"47F=$\"0Eo![.J#*\\Fdt7 $$!0E:7j')Hg#F=$\"0OSG:A]-&Fdt7$$!0D5-`#>HiF=$\"0/_ojo!H]Fdt7$$!0r%eHI%f;0]Fdt7$$!0qv-&pNw8Fdt$\"02[zxMP&\\Fdt7$$!0XTF=RQw\"F dt$\"0Qmes\\+([Fdt7$$!0Cc!*G/D8#Fdt$\"0j[0l_1w%Fdt7$$!06]pucE]#Fdt$\"0 Utzv)y>YFdt7$$!00'[k#zq:`$Fdt$\"0e%H=K))QSFdt7$$!0u;Nlg<$QFdt$\"07I*eIQ0QFdt7$ $!0u'*)3_tMTFdt$\"0\\mB0N=`$Fdt7$$!02;rtzjS%Fdt$\"0.\"\\-2QZKFdt7$$!0( QV%R2\\o%Fdt$\"0pw,P=r!HFdt7$$!0r\"\\@J#[!\\Fdt$\"0QE`s?Jf#Fdt7$$!0gk[ jR(G^Fdt$\"0;X&eQt;AFdt7$$!0],$\\#fvI&Fdt$\"0-)>M\\)o&=Fdt7$$!0R\"p5Z0 uaFdt$\"0[a(e*ypW\"Fdt7$$!0UO\"fs<#f&Fdt$\"0llRDy83\"Fdt7$$!0odu;wnp&F dt$\"0qVdYEo`'F=7$$!0a#)**f(fmdFdt$\"0&4uTX78BF=7$$!0#Rx`%G\\!eFdt$!0? <[%oOv>F=7$$!0[UtvV7\"eFdt$!0=^7Sh=H'F=7$$!0\"znW&Rpy&Fdt$!0@'\\fnwX5F dt7$$!0\")*ye1#ps&Fdt$!0k0;D%o&\\\"Fdt7$$!0tge!>,PcFdt$!0W3F1P;#>Fdt7$ $!0\")oeVI!3bFdt$!0)*)z\"[iUO#Fdt7$$!0ESq=i6O&Fdt$!0+c@\\[wv#Fdt7$$!0, ]zPng;&Fdt$!0@[CG'z\"=$Fdt7$$!0gb1[7w%\\Fdt$!0.4%*zd^d$Fdt7$$!0R\")*)e a(*p%Fdt$!0'R![/0E&RFdt7$$!0SOXDd+T%Fdt$!0-aUsB%GVFdt7$$!0aUkH]l6%Fdt$ !0#Fdt$!0d)otN79gFdt7$$!0h3Rv&=#y\"Fdt$!0/!)*ePu%='Fdt7$$!0 iRZB**)G8Fdt$!0R!=1jUNjFdt7$$!005_#\\Sm')F=$!0DH)*>t>X'Fdt7$$!0nP'Hc37 OF=$!0jVq)*=\"RlFdt7$$\"0*zv0](R=*F0$!0Bo=58Ie'Fdt7$$\"0mf9#e6)>'F=$!0 olh!>Z%f'Fdt7$$\"07S^f4%)4\"Fdt$!0s(\\moJolFdt7$$\"0P*f;DRr:Fdt$!0nJb$ o63lFdt7$$\"0)4$RdQl2#Fdt$!0)zx4uB0kFdt7$$\"0\\8T0%3xDFdt$!0zGE9XBE'Fd t7$$\"0n\"y(R+T-$Fdt$!0Tx#y\"4#)4'Fdt7$$\"0XCB)oN([$Fdt$!0qF8xq)))eFdt 7$$\"01w!=S\\DRFdt$!0Gs=5K0l&Fdt7$$\"0%\\b6I$>Q%Fdt$!0`Cm`y_N&Fdt7$$\" 0bf\"G$4!fZFdt$!0zY:m/*p]Fdt7$$\"0\"4x**z)*o^Fdt$!0ZMxj*Q4ZFdt7$$\"0C8 6\"zVHbFdt$!0y^U'=:SVFdt7$$\"04+Bs?.'eFdt$!07()=zWs%RFdt7$$\"0Gs*3sSjh Fdt$!0hjFW[(GNFdt7$$\"0Ao')z=;W'Fdt$!0OQTeZz2$Fdt7$$\"0zXXGQ.q'Fdt$!0+ ZIcGid#Fdt7$$\"028uY?J!pFdt$!0.vLqXq4#Fdt7$$\"0zy3%ybpqFdt$!0D*3#RS%3; Fdt7$$\"0'G+,114sFdt$!0mHY\"3rr5Fdt7$$\"0RVS4'[2tFdt$!0b!3+\\^U_F=7$$ \"0]H$3o2itFdt$\"0Y$\\A2#G:%!#A-%'COLOURG6&%$RGBG$\"\"!FdjnFcjn$\"*+++ +\"!\")-F$6%7Z7$$\"\"\"FdjnFcjn7$$\"0+++++++\"FdtF\\[o7$$\"0_M\")=K*GH F=$\"0b'=\"y1rq\"Fdt7$$!0O+%3M0FpF=$\"0J7*f(3i(=Fdt7$$!0>'z?(43j\"Fdt$ \"0H#\\*3c)H:Fdt7$$!0avJ;#)\\J#Fdt$\"0X(y1\"e`+)F=7$$!0DS$R&*zTEFdt$!0 1?*)*p^X9F=7$$!0)zEKT;(e#Fdt$!0wu02eI9\"Fdt7$$!0Erd2KI=#Fdt$!0Tf:sex0# Fdt7$$!08=>]7r\\\"Fdt$!0$)\\,3Oay#Fdt7$$!0Z'4HF!G;'F=$!0G2@ik)eKFdt7$$ \"0C))4\"Q/jOF=$!0-He6!oWMFdt7$$\"0%=[ Fdt7$$!0^d&>.+v5F=$\"0+N2CW))*\\Fdt7$$!0v-,))os5\"Fdt$\"0&QMMUMx\\Fdt7 $$!0f%f%R1M3#Fdt$\"0K>5%4>gZFdt7$$!05D$ob]**HFdt$\"0zNM>R#fVFdt7$$!0;f 0MCL#QFdt$\"0nDF#fQ#z$Fdt7$$!0gxps_v_%Fdt$\"0)\\M;CT#3$Fdt7$$!0l*Hk;K! 4&Fdt$\"0w\"Rj\")zbAFdt7$$!02ZZ(\\Z&\\&Fdt$\"0zhMS\\:M\"Fdt7$$!0Ao[kHE t&Fdt$\"0I1M)\\x+PF=7$$!0J,$o=0(z&Fdt$!0!=+FBXyiF=7$$!0w/#*Hx$*o&Fdt$! 0f6hUJ?i\"Fdt7$$!0W))p%R?:aFdt$!0MZBr6Pe#Fdt7$$!0*QEG`e%)\\Fdt$!027NqX i[$Fdt7$$!0&)3^1]9T%Fdt$!0!eh$[1dI%Fdt7$$!0vk.CsHr$Fdt$!0:DC=Q8-&Fdt7$ $!0-#eFY\"*3HFdt$!0I/Cd*)eh&Fdt7$$!0oU2_k4-#Fdt$!0G6&f$He2'Fdt7$$!0cuI Rz?2\"Fdt$!02f8*4X\"R'Fdt7$$!00K*)R4de)F0$!0!e8Lk(ob'Fdt7$$\"0R9\"z=dS \"*F=$!04As^p*plFdt7$$\"0r(Rft^/>Fdt$!0,[8@q@V'Fdt7$$\"0GfF dt7$$\"03.aE)z2sFdt$!0VM9!\\aB5Fdt7$$\"0\"4HqHR[tFdt$!0IGqomxM$F07$$\" 0v8Pq[HN(Fdt$\"0hBsb>^m*F=7$$\"0L!>eUiAsFdt$\"0(4ncL)z&>Fdt-F`jn6&Fbjn FejnFcjnFcjn-%*THICKNESSG6#\"\"#-%*AXESSTYLEG6#%%NONEG-%(SCALINGG6#%,C ONSTRAINEDG-%%VIEWG6$%(DEFAULTGF`]p" 1 2 0 1 10 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "1.0788914983295;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#$\"/&H$)\\\"*)y5!#8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "ev alf(2157782996659/2,20);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"5+++&H$ )\\\"*)y5!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "series(t(n ),n=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"#\"\"\"*&F&F &%\"nG!\"\"#F)F%F&-%\"OG6#F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "limit(sqrt(n)-t(n)/2,n=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(#\"#Z\"#'*\"\"\"*(\"\"$F'\"#;!\"\"%#PiGF'F'*&#F'\"\"# F'-%\"OG6#F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "sum((-1 )^(k+1)/sqrt(k),k=1..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$ sumG6$*&)!\"\",&%\"kG\"\"\"F+F+F+F*#F(\"\"#/F*;F+%)infinityG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "tt:=n->sum(1/sqrt(k),k=1..n- 1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ttGf*6#%\"nG6\"6$%)operatorG %&arrowGF(-%$sumG6$*&\"\"\"F0-%%sqrtG6#%\"kG!\"\"/F4;F0,&9$F0F0F5F(F(F (" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "series(sqrt(n)-tt(n)/2 ,n=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.*&#\"\"\"\"\"#F&-%% ZetaG6##F&F'F&!\"\"*&\"\"%F,*&F&F&%\"nGF,F+F&*&\"#[F,F/#\"\"$F'F&*&\"$ o(F,F/#\"\"(F'F,*&\"%[?F,F/#\"#6F'F&-%\"OG6#*$)F/#\"#:F'F&F&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "seq(evalf(tt(n)/2-t(n)/2),n= 1000);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Izs\"Q$!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "seq(evalf(tt(n)/2-t(n)/2),n=10000); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+c&4QX$!#5" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 81 "t:=n->if n=0 then 0 else sum(evalf(arctan(1/ sqrt(k))),k=1..n-1) fi;r:=n->sqrt(n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"tGf*6#%\"nG6\"6$%)operatorG%&arrowGF(@%/9$\"\"!F/-%$sumG6$-%&ev alfG6#-%'arctanG6#*&\"\"\"F:-%%sqrtG6#%\"kG!\"\"/F>;F:,&F.F:F:F?F(F(F( " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rGf*6#%\"nG6\"6$%)operatorG%&a rrowGF(-%%sqrtG6#9$F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "seq(evalf(r(n)-t(n)/2),n=10000);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#$\"+]%e!y5!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "seq(eva lf(r(n)-t(n)/2),n=20000);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+44Iy5 !\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Mk)*[g!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "evalf(Sum((-1)^k*Zeta(k + 1/2)/(2*k + 1), k= 0..infin ity));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+(*Hyd@!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "zeta" }}}}{MARK "2 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }