Mathematics - Limits Question with Solution | TestHub

${\mathrm{Lim}}_{n\to \infty }\left\{{\left(\frac{1}{n}\right)}^4+{\left(\frac{2}{n}\right)}^4+{\left(\frac{3}{n}\right)}^4+\dots \dots \dots .{\left(\frac{n}{n}\right)}^4\right\}-{\mathrm{Lim}}_{n\to \infty }\frac{1}{n}\left\{\frac{1}{n^4}+\frac{2^3}{n^4}+\dots \dots .\cdot \frac{n^3}{n^4}\right\}$ ${\int }_0^1(x{)}^{4}dx-0={\left[\frac{x^5}{5}\right]}_0^1=\frac{1}{5}$