Find all such that the series

converges and compute the sum.

First, we apply the ratio test,

Thus, the series converges for . For the boundary, if then this is the alternating harmonic series which converges. If then it is the harmonic series, which diverges. Therefore, the series converges for all . Then, we compute,

*Related*

The RHS of P'(x) should be multiplied by 2 in the first 2 rows. Later it’s correct.