What have you tried? Where are you stuck? I hope that you just don't expect that someone does this for you as that would not help you very much.
So please show us what you can do.
Clearly the series with an alternating null sequence converges,
Lets look at the \(\displaystyle \frac{1}{(2k + 1)(2k + 2)}\) as a partial fractions. We get \(\displaystyle \frac{1}{2k+1}-\frac{1}{2k+2}\). Look at this solution.
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