Summation to n of kth Harmonic Number over k

Theorem

 * $\displaystyle \sum_{k \mathop = 1}^n \dfrac {H_k} k = \dfrac { {H_n}^2 + H_n^{\paren 2} } 2$

where:
 * $H_n$ denotes the $n$th harmonic number
 * $H_n^{\paren 2}$ denotes a general harmonic number.

Proof
Hence the result.