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- #1

- Jan 26, 2012

- 4,198

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For each positive integer $k$, let $A(k)$ be the number of odd divisors of $k$ in the interval $[1, \sqrt{2k}\,)$. Evaluate

\[

\sum_{k=1}^\infty (-1)^{k-1} \frac{A(k)}{k}.

\]

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