The first series is one around and its convergence radius is , since you got .

Besides this, the series converges at (you get the alternating harmonic series), but diverges at (you get the harmonic series), so the interval of conv. is .

The second question is written, apparenty, in sumerian mixed with ancient sanscrit, but if I have to guess you're asked to find a power series for that function h(x), and yes: what you did is correct.

Tonio