For the series _ k=1 ^ (-1)^ k+1 x^ k k , 0<x 1

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

Problem

For the series ∑k=1∞(−1)k+1xkk,0<x≤1,\sum_{k=1}^{\infty}(-1)^{k+1}\frac{x^{k}}{k}, \qquad 0<x\le 1, write the inequality that must hold between consecutive term magnitudes to confirm that the terms form a decreasing sequence, and state that inequality explicitly.

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