Question Number 192453 by Spillover last updated on 18/May/23
$${Find}\:\:\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} }+\frac{\mathrm{2}}{{n}^{\mathrm{2}} }+\frac{\mathrm{3}}{{n}^{\mathrm{2}} }+…\frac{{n}}{{n}^{\mathrm{2}} }\right) \\ $$
Answered by senestro last updated on 18/May/23
$$\mathrm{1}/\mathrm{2} \\ $$
Answered by AST last updated on 18/May/23
$$\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\left(\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}}\right)=\frac{{n}+\mathrm{1}}{\mathrm{2}{n}}=\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}{n}}\Rightarrow\underset{{n}\rightarrow\infty} {{lim}}\left(\underset{{p}=\mathrm{1}\:} {\overset{{n}} {\sum}}\frac{{p}}{{n}^{\mathrm{2}} }\right)=\frac{\mathrm{1}}{\mathrm{2}} \\ $$
Commented by Spillover last updated on 19/May/23
$${great}. \\ $$