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I've been skimming through Knopp's book "Theory and Applications of Inifnite Series", mostly to get some practice with sequences/series. The problems there are pretty hard, I've been trying to do this one without much success. It is from Chapter 2, 15(b): show that the following sequence converges to 1/2

[tex]\log\left(1+\frac{1}{n^2}\right) + \log\left(1+\frac{2}{n^2}\right) + ... + \log\left(1+\frac{n}{n^2}\right)[/tex]

Does anyone have an idea how to do this?

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# Limit of a sequence from Knopp

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