limn→∞ 2n+5n1/n is equal to

$lim_{n \to \infty} {(2^{n} + 5^{n})}^{1 / n}$ is equal to

A
2
B
5
C
$e$
D
none of these

Solution:

We have,

$lim_{n \to \infty} {(2^{n} + 5^{n})}^{1 / n} = lim_{n \to \infty} 5 {\{1 + {(\frac{2}{5})}^{n}\}}^{1 / n} = 5 \times 1^{0} = 5$

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