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