Summation to n of Power of k over k

Theorem

 * $\displaystyle \sum_{k \mathop = 1}^n \dfrac {x^k} k = H_n + \displaystyle \sum_{k \mathop = 1}^n \dbinom n k \dfrac {\left({x - 1}\right)^k} k$

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