Mathematics

Problem

The series

\displaystyle \sum_{n=1}^{\infty} (-1)^{n+1}\frac{1}{2n-1}

converges to

\pi/4

. Let

S_5

and

S_7

be the partial sums through the 5th and 7th terms, respectively. Calculate the alternating-series error bound for each partial sum and indicate which approximation is closer to

\pi/4

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