Limit Integral Difficult

Problem - 4547

Evaluate $\displaystyle\lim_{n\to\infty}S_n$ where

$$S_n = 1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\cdots + (-1)^{n-1}\frac{1}{n}$$

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