Question Number 159936 by qaz last updated on 22/Nov/21
$$\mathrm{Prove}::\:\:\:\underset{\mathrm{n}\rightarrow+\infty} {\overline {\mathrm{lim}}n}\underset{\mathrm{k}=\mathrm{n}+\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{k}−\mathrm{1}} }{\mathrm{k}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$