Question Number 217378 by MrGaster last updated on 12/Mar/25
![Whether the following seriesconverge: determinant (((Σ_(n=1) ^∞ (−1)^n [1+n ln(1−(2/(2n+1)))])))](https://www.tinkutara.com/question/Q217378.png)
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Whether}\:\mathrm{the}\:\mathrm{following}\: \\ $$$$\mathrm{seriesconverge}: \\ $$$$\begin{array}{|c|}{\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \left[\mathrm{1}+{n}\:\mathrm{ln}\left(\mathrm{1}−\frac{\mathrm{2}}{\mathrm{2}{n}+\mathrm{1}}\right)\right]}\\\hline\end{array} \\ $$