MCQ
$\mathop {\lim }\limits_{n \to \infty } {({4^n} + {5^n})^{1/n}}$ is equal to
- A$4$
- ✓$5$
- C$e$
- DNone of these
$ = \mathop {\lim }\limits_{n \to \infty } \,5\,{\left[ {{{\left\{ {1 + {{\left( {\frac{4}{5}} \right)}^n}} \right\}}^{{{(5/4)}^n}}}} \right]^{(1/n)\,.\,{{(4/5)}^n}}} = 5\,.\,{e^0} = 5$.
$\left( {\because \,\,{{\left( {\frac{4}{5}} \right)}^n} \to 0\,{\text{as }}\,n \to \infty } \right)$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.