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{SECT 0 {PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 263 "" 0 "" {TEXT -1 
23 "Calulus Worksheet VII\n\n" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 75 "
In this worksheet we give a few examples how Maple handles infinite se
ries." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "a:=n->1/n^2:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Sum(a(n),n=5..9)=sum(a(n),n=
5..9):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "Sum(a(n),n=1..inf
inity)=\nsum(a(n),n=1..infinity):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 52 "Sum(1/n,n=1..1000000)=\nevalf(sum(1/n,n=1..1000000)):
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "a:=n->r^n:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Sum(a(n),n=0..N)=sum(a(n),n=0..N):
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "Sum(a(n),n=0..infinity)
=\nsum(a(n),n=0..infinity):" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 19 "
Taylor polynomials:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "taylo
r(sin(x),x=0,10):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "conver
t(\",polynom):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "taylor(si
n(x),x=Pi/2,8):" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 34 "Convergence \+
of Taylor polynomials:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "wi
th(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 166 "plot(\{seq(
\nconvert(\ntaylor(sin(x),x=0,2*n+1),\npolynom),\nn=1..5),\nsin(x)\},x
=-2*Pi..2*Pi,\nview=[-2*Pi..2*Pi,-1.2..1.2],\nnumpoints=200,\nscaling=
constrained,thickness=2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
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