(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove: [tex]\sum_{i=1}^{\infty}\sum_{j=1}^{i-1} \frac{(-1)^i}{i j}=\frac{1}{2}\ln^2 2[/tex]

2. Relevant equations

[tex]\ln 2 = \sum_{i=1}^{\infty} \frac{(-1)^{i+1}}{i}[/tex]

3. The attempt at a solution

I'm trying to manipulate the l.h.s. of the problem to transform it into [tex]\frac{1}{2}\sum_{i=1}^{\infty}\sum_{j=1}^{\infty} \frac{(-1)^{i+j}}{i j}[/tex] but I just can't seem to get it.

Any suggestions will be appreciated.

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# Homework Help: Sum of a series resulting in a logarithm

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