For (|x|<1 )

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

Problem

For ∣x∣<1|x|<1, let h(x)=∑n=1∞(−1)n+1xnnh(x)=\displaystyle\sum_{n=1}^{\infty}(-1)^{n+1}\frac{x^{n}}{n}. Determine the smallest positive integer NN such that the magnitude of the term (−1)N+2(0.5)N+1N+1\displaystyle(-1)^{N+2}\frac{(0.5)^{N+1}}{N+1} is less than 10−410^{-4}, and state that value of NN.

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