Summation to n of Power of k over k

Theorem

 * $\ds \sum_{k \mathop = 1}^n \dfrac {x^k} k = H_n + \sum_{k \mathop = 1}^n \dbinom n k \dfrac {\paren {x - 1}^k} k$

where:
 * $H_n$ denotes the $n$th harmonic number
 * $\dbinom n k$ denotes a binomial coefficient.