Thursday
April 24, 2014

Homework Help: Math

Posted by Sean on Thursday, May 28, 2009 at 12:28pm.

What does the following infinite series starting at k=2 converge to: Σ ln (1 - 1/k^2)

In other words, what does this converge to: ln(1 - 1/4) + ln(1 - 1/9) + ln(1 - 1/16) + ln(1 - 1/25) + ln(1 - 1/36) + ...

I assume the first step is this:
Σ ln (1 - 1/k^2) = ln Π (1 - 1/k^2)

But from there, I don't know how to convert this to closed form and continue.

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