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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "Mat1505 04S Quiz 7 NOT! (d
ownload first part of worksheet from homework log)" }}}{EXCHG {PARA 0
"" 0 "" {TEXT -1 30 "Exploring a series with Maple:" }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 23 "a:=n->(-1)^(n-1)/n/2^n;" }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 23 "S:=n->sum(a(k),k=1..n);" }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 43 "array([seq(evalf([n,a(n),S(n)]),n=1..12)]
);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "The 11th term is less than \+
one half times 10^(-4), so S_10 should be enough (N = 10):" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "evalf(S(10)); evalf(%,4);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 82 "However, the roundoff changes the \+
last digit from the roundoff of the true result:" }}}{EXCHG {PARA 0 ">
" 0 "" {MPLTEXT 1 0 47 "sum(a(n),n=1..infinity);\nevalf(%); evalf(%,
4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 ".4054651081-.4054;\n
.4054651081-.4054346478;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 156 "Clea
rly the unrounded result is closer to the true one, so if you are goin
g to use this number inside of a larger calculation, it is better not \+
to round it." }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
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