Want to show $\sum_{n=2}^{\infty} \frac{1}{2^{n}*n}$ converges Want to show $\sum_{n=2}^{\infty} \frac{1}{2^{n}*n}$ converges. I am trying to show this by showing that the partial sums are bounded. I have tried doing this by induction but am not seeing how to pass the inductive assumption part. Do I need to instead look for a closed form? thanks

Or we can go this way
$$\sum_{n=2}^{\infty} \frac{1}{n2^{n}}\le\sum_{n=2}^{\infty} \frac{1}{n^2}\le \sum_{n=2}^{\infty} \frac{1}{n(n-1)}=1$$
and the sum is precisely $\log 2-\frac{1}{2}$ (hint: use the Taylor expansion of $\ln(1-x), |x|<1)$
Chris.
