Question Number 79652 by john santu last updated on 27/Jan/20
![what is the value of Σ_(n=1) ^∞ [(4n^2 −1)ln(1−(1/(4n^2 )))+1]](https://www.tinkutara.com/question/Q79652.png)
$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\left[\left(\mathrm{4n}^{\mathrm{2}} −\mathrm{1}\right)\mathrm{ln}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{4n}^{\mathrm{2}} }\right)+\mathrm{1}\right]\: \\ $$