Question Number 144877 by imjagoll last updated on 30/Jun/21
$$\:\:\mathrm{u}+\sqrt{\mathrm{u}}+\sqrt[{\mathrm{3}}]{\mathrm{u}}+\sqrt[{\mathrm{4}}]{\mathrm{u}}+\sqrt[{\mathrm{5}}]{\mathrm{u}}+...\:+\infty=? \\ $$$$ \\ $$
Answered by MJS_new last updated on 30/Jun/21
$$\forall{u}>\mathrm{0}:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{u}^{\mathrm{1}/{n}} \:=+\infty \\ $$$$\mathrm{easy}\:\mathrm{to}\:\mathrm{see}\:\mathrm{because}\:\underset{{n}\rightarrow+\infty} {\mathrm{lim}}{u}^{\mathrm{1}/{n}} \:=\mathrm{1} \\ $$
Commented by imjagoll last updated on 30/Jun/21
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir} \\ $$