ILL 1970 Problem 9

For even $n$ , prove that $\sum_{i=1}^{n}{\left((-1)^{i+1}\cdot\frac{1}{i}\right)}=2\sum_{i=1}^{n/2}{\frac{1}{n+2i}}$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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