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By Sterl Phinney 2/13/2004." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 105 "We wis h to expand terms of the geometric series Sum_k=1,n x^k, and compare \+ it to 1/(1-x) for various n:]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "Geomser := (x,n) -> Sum(x^k,k=0..n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(GeomserGf*6$%\"xG%\"nG6\"6$%)operatorG%&arrowGF)-%$S umG6$)9$%\"kG/F2;\"\"!9%F)F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "We now compare the two functions for n=7, with the series in blue and 1/(1-x) in red." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "plot([G eomser(x,7),1/(1-x)],x=0..1, y=0..5,linestyle=[1,4],color=[blue,red]); " }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6& -%'CURVESG6%7gn7$$\"\"!F)%%FAILG7$$\"3/LL3x1h6o!#@$\"3bpVOD;o+5!#<7$$ \"3hmmTN@Ki8!#?$\"3PH))e!=k8+\"F17$$\"3\"***\\7.K[V?F5$\"3.Dudnw/-5F17 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