How to compute the sum of a series How to compute the sum of the following series.
I have no idea...
The series is $$\sum_{n=1}^\infty(1+1/2+\cdots+1/n)x^n.$$

Outline: Note that the Maclaurin series for $-\ln(1-x)$ is
$$x+\frac{x^2}{2}+\frac{x^3}{3}+\frac{x^4}{4}+\frac{x^5}{5}+\cdots,$$
and the Maclaurin series for $\frac{1}{1-x}$ is
$$1+x+x^2+x^3+x^4+\cdots.$$
Multiply.
