Question Number 126607 by shaker last updated on 22/Dec/20 | ||
Answered by Olaf last updated on 22/Dec/20 | ||
$$\underset{\infty} {\sim}\:\frac{{x}^{\mathrm{1}+\mathrm{2}+\mathrm{3}+...+{n}} }{\left[\left({nx}\right)^{{n}} \right]^{\frac{{n}+\mathrm{1}}{\mathrm{2}}} }\:=\:\frac{{x}^{\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}}} }{{n}^{\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}}} {x}^{\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}}} }\:=\:\frac{\mathrm{1}}{{n}^{\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}}} } \\ $$ | ||