Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 205367 by hardmath last updated on 18/Mar/24

Answered by Ghisom last updated on 18/Mar/24

$${(\frac{n^{3/2}}{3^n}+\frac{n^2}{4^n}+\frac{n^{5/2}}{5^n})}^{1/n}=$$$$=\frac{n^{3/\left(2n\right)}}{60}{({20}^n+{15}^n{n}^{1/2}+{12}^{n}n)}^{1/n}$$$$n\to \mathrm{\infty }\Rightarrow \{\begin{array}{l}{n}^{3/\left(2n\right)}\to 1\\ {({20}^n+...)}^{1/n}\to 20\end{array}$$$$\Rightarrow \lim =\frac{20}{60}=\frac{1}{3}$$

Commented by hardmath last updated on 21/Mar/24

$$\mathrm{thank}\mathrm{you}\mathrm{dear}\mathrm{sir}$$

Commented by Ghisom last updated on 22/Mar/24

$${\mathrm{you}}^{\prime }\mathrm{re}\mathrm{welcome}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com