\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Consider an infinite series of the form

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$$
\pm3\pm1\pm{1\over3}\pm{1\over9}\pm
{1\over{27}}\pm\cdots\pm{1\over{3^n}}\pm\cdots\,.$$

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\noindent The numbers $3$, $1$, etc., are given but {\it you}\/ will
decide what the signs should be.

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\noindent a) Can you choose the signs to make the series diverge?

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\noindent b) Can you choose the signs to make the series sum to $3.5$?

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\noindent c) Can you choose the signs to make the series sum to $2.25$?

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\noindent In each case, if your answer is ``Yes'', then specify how to
choose the signs; if your answer is ``No'', then explain.

\vfil\eject\end