Question Number 6009 by FilupSmith last updated on 09/Jun/16
$$\mathrm{Is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{to}: \\ $$$${S}=\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{i}^{{k}} ,\:\:\:\:\:{k}\in\mathbb{Z},\:{k}\geqslant\mathrm{1} \\ $$