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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 15 "Harmonic series" }}{PARA 
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256 "" 0 "" {XPPEDIT 18 0 "1 + 1/2 + 1/3 + 1/4" "6#,*\"\"\"F$*&F$F$\"
\"#!\"\"F$*&F$F$\"\"$F'F$*&F$F$\"\"%F'F$" }{TEXT -1 6 " + ..." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 13 "is called
 the" }{TEXT 256 16 " harmonic series" }{TEXT -1 78 ".  We can compute
 values of its partial sums by the following Maple procedure." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 194 "Harmonic := proc(n::posint)
\n            local N,j, sum;\n            sum:=0.;\n            for j
 to n do\n                 sum := sum + evalf(1/j):\n            od;\n
            sum;\n            end;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "The first val
ues of the partial sums of the harmonic series are" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 41 "for j from 5 to 15 do Harmonic(10*j); od;" }}{PARA 
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0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 96 "Even though we step, in \+
the above, by 10 each time, the harmonic series appears to stay bounde
d." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 159 "Th
is is, however, an illusion.  Maple actually knows that the harmonic s
eries diverges, a fact that is not apparent from numerical computation
s.  In particular" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 37 "Sum(1/n,n=1..infinity): % = value(%);" }}}
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