A) \[4\]
B) 5
C) \[e\]
D) None of these
Correct Answer: B
Solution :
Given limit \[=\underset{n\to \infty }{\mathop{\lim }}\,\,{{({{4}^{n}}+{{5}^{n}})}^{1/n}}\] \[=\underset{n\to \infty }{\mathop{\lim }}\,\,5\,{{\left[ {{\left\{ 1+{{\left( \frac{4}{5} \right)}^{n}} \right\}}^{{{(5/4)}^{n}}}} \right]}^{(1/n)\,.\,{{(4/5)}^{n}}}}=5\,.\,{{e}^{0}}=5\] . \[\left( \because \,\,{{\left( \frac{4}{5} \right)}^{n}}\to 0\,\text{as }\,n\to \infty \right)\]
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