I must find sum of this functional serie. I don't know what to do here.

Question

x+x²/2+x³/3+x⁴/4+...+xⁿ/n and x∈(-1,1)

Answer 1

Take the derivatives term by term, and you end up with 1+x+x^2+...=1/(1-x). Integrating from 0 to x yields -ln(1-x).