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\noindent {\bf Problem statement} The series $\sum\limits_{n=1}^\infty
{{(-1)^{n+1}}\over n}$ and $\sum\limits_{n=1}^\infty {1\over{n2^n}}$
both converge (why?). By coincidence it turns out that their sums are
both equal to $\ln 2$. (You'll understand this coincidence when we
study Taylor series.)

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\noindent Which series converges ``faster'' (and so numerically gives
a more efficient way to get a numerical approximation for $\ln 2$)?
Justify your answer by computing how many terms of each series must be
added up to approximate $\ln 2$ with maximum allowed error of
$10^{-6}$.

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