The harmonic numbers $H_n$ are defined by $H_0=1$ and $$H_n = 1+\dfrac{1}{2}+\dfrac{1}{3}+\dots+\dfrac{1}{n-1}+\dfrac{1}{n}.$$ Find the formula for the power series $H(z)=\displaystyle\sum\limits_{n=0}^\infty H_n z^n$
This is the first time I encounter the harmonic numbers so I got no idea on how to do this. Can somebody please help me with this? Any idea is appreciated.