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{SECT 0 {EXCHG {PARA 18 "" 0 "top_s10_3" {TEXT -1 27 "10.3  Convergenc
e of Series" }}{PARA 19 "" 0 "" {TEXT -1 25 "Art Belmonte, Summer 1996
" }}{PARA 0 "" 0 "" {TEXT -1 64 "These are the shaded gray examples wh
ich appear in Section 10.3." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
34 "restart; a:=n->2^(3*n) / (2*n+1)!;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"aG:6#%\"nG6\"6$%)operatorG%&arrowGF(*&)\"\"#,$9$\"\"$\"\"\"-
%*factorialG6#,&F0F.F2F2!\"\"F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 41 "Limit(a(n+1)/a(n), n=infinity); value(\");" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#-%&LimitG6$**)\"\"#,&%\"nG\"\"$F+\"\"\"F,-%*
factorialG6#,&F*F(F+F,!\"\")F(,$F*F+F1-F.6#,&F*F(F,F,F,/F*%)infinityG
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 40 "Limit(a(n)^(1/n), n=infinity); value(\");" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#-%&LimitG6$)*&)\"\"#,$%\"nG\"\"$\"\"\"-%*fac
torialG6#,&F+F)F-F-!\"\"*$F+F2/F+%)infinityG" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "a:=
n->ln(n) / n^2; b:=n->1/n^(3/2);\nLimit(a(n)/b(n), n=infinity); value(
\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG:6#%\"nG6\"6$%)operatorG
%&arrowGF(*&-%#lnG6#9$\"\"\"F0!\"#F(F(" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"bG:6#%\"nG6\"6$%)operatorG%&arrowGF(*$9$#!\"$\"\"#F(F(" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%&LimitG6$*&-%#lnG6#%\"nG\"\"\"F*#!\"
\"\"\"#/F*%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Int(a(n), n=1..infinity); va
lue(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$*&-%#lnG6#%\"nG\"
\"\"F*!\"#/F*;F+%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "6 0 0" 0 }
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