The partial sum of the series is

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

The partial sum S7S_{7} of the series ∑k=1∞(−1)k+11k2\sum_{k=1}^{\infty} (-1)^{k+1}\frac{1}{k^{2}} is 0.9478320.947832. How many decimal places in this approximation are guaranteed to be correct?

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