For the alternating harmonic series

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

Problem

For the alternating harmonic series ∑n=1∞(−1)n+11n\displaystyle \sum_{n=1}^{\infty} (-1)^{n+1} \frac{1}{n}, let S7S_7 and S8S_8 denote the partial sums obtained by truncating after the 7th and 8th terms, respectively. Identify which partial sum is guaranteed to be closer to the exact value of the series and state the reason in one concise sentence.

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