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## Homework Statement

Test for convergence or divergence. Give a reason for your decision.

## Homework Equations

[itex]\sum_{i=1}^{\infty} \frac{\sqrt{2n-1} \log{(4n + 1)}}{n(n + 1)}[/itex]

## The Attempt at a Solution

I've tried to compare it to the series [itex]\sum_{i=1}^{\infty} \frac{\sqrt{2n-1} \log{(4n + 1)}}{n^2}[/itex] and show the latter converges. I have no idea how to show this. Although the limit of the sequence approaches 0 as n goes to infinite, that is not enough to guarantee convergence. The book says it converges.

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