\input epsf
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\noindent {\bf Problem statement} Consider the series

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\settabs 3 \columns
\+a)$\displaystyle\sum_{n=1}^\infty {{(-1)^n}\over{\sqrt{n}+1}}$
&b) $\displaystyle\sum_{n=1}^\infty {{(-1)^n\sin n}\over{n^6+1}}$
&c) $\displaystyle\sum_{n=1}^\infty {{(-1)^n}\over{(n!)^2}}$\cr

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\noindent a) Decide for each series if the conditions
of the alternating series test are satisfied.

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\noindent b) For those series satisfying the conditions, decide how
many terms need to be added in order to reach within $10^{-8}$ of
the sum of the series. Give a decimal approximation of the sum of {\it
one}\/ of the series with maximum allowed error of $10^{-8}$.

\vfil\eject\end