what is the summation of \(\sum_{n=1}^\infty \log\left(\dfrac{n(n+2)}{(n+1)^2}\right) \)?
what is the summation of \(\displaystyle\sum_{n=1}^{\infty} (\sqrt[n]{2} - 1) \)?
what is the summation of \(\displaystyle\sum_{n=1}^{\infty}\dfrac{1}{n^{(n+1)/n}} \)?
If there is no explicit answer just say it converges.
