{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{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 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "One way to produce a list \+ in Maple is to use the dollar sign, $ . " }}{PARA 0 "" 0 "" {TEXT 257 8 "Sequence" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "n/(n+1) \+ $n=3..7;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "a := [[n, n^2] \+ $n=1..10];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plot(a, x=0.. 12, style=point);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "b := [ [n, n/(n+1)] $n=1..10];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " plot(b, x=0..12, style=point);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "c := [[n, (-1)^n/(n!)] $n=1..10];" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 29 "plot(c, x=0..12, style=line);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 25 "Investigate the number e:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "d:=[[n ,evalf((1+1/n)^n)] $n=1..100];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "plot(\{d,exp(1)\}, x=1..100, style=point);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 256 6 "Series" }}{PARA 0 "" 0 "" {TEXT -1 28 "Example: A geometric series." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "s:=proc(n) sum((1/2)^k,k=1..n) end;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "t:=[[n,evalf(s(n))] $n=1..10 0];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "plot(\{t,1\}, x=1..1 00, style=point);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 8 "Example:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "s:=proc(n) sum(((-1)^k)*(1/k), k=1..n) end;" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 31 "t:=[[n,evalf(s(n))] $n=1..100];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "plot(\{t,-0.69\}, x=1..100, style=p oint);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "Example:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "s:=proc(n) sum((1/k^2), k=1..n) end ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "t:=[[n,evalf(s(n))] $n =1..100];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "plot(\{t,1.64 \}, x=1..100, style=point);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "evalf(sum(1/k^2,k=1..infinity));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "Int(1/x^2,x=0..infinity);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "evalf(int(1/x^2,x=1..infinity));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "evalf(int(1/x^2,x=0..1));" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{MARK "30" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }