A Putnam Problem

Calculus Level 5

∑k=1∞∑n=0∞(−1)k−1k(1+2nk)\large \sum_{k = 1}^{\infty} \sum_{n = 0}^{\infty} \frac{(-1)^{k - 1}}{k(1 + 2^nk)}

Find the value (to 2 decimal places) of the closed form of the expression above.

Source: This is problem B6 of the Putnam 2016 competition.
Deeparaj Bhat by Deeparaj Bhat
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