A Proof of Bala's General-$m$ Representation of the Harmonic Numbers

Tong Niu

For every nonzero integer $m$ and every integer $n\ge 1$, the $n$\textsuperscript{th} harmonic number $H_n=1+\frac{1}{2}+\cdots +\frac{1}{n}$ satisfies the identity \[ H_n \;=\; \…