Summation to n of Reciprocal of k by k-1 of Harmonic Number

Theorem

 * $\displaystyle \sum_{1 \mathop < k \mathop \le n} \dfrac 1 {k \paren {k - 1} } H_k = 2 - \dfrac {H_n} n - \dfrac 1 n$

where $H_n$ denotes the $n$th harmonic number.