Question Number 160885 by qaz last updated on 08/Dec/21
$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{n}+\frac{\mathrm{1}}{\mathrm{k}}}{\:\sqrt{\mathrm{n}^{\mathrm{2}} +\mathrm{k}^{\mathrm{2}} }}\centerdot\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{n}}=? \\ $$