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Let $\mathrm{x}_{\mathrm{n}}=\left(2^{\mathrm{n}}+3^{\mathrm{n}}\right)^{1 / 2 \mathrm{n}}$ for all natural numbers $\mathrm{n}$. Then
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The correct answer is:
$\lim _{n \rightarrow \infty} x_{n}=\sqrt{3}$
$\lim _{n \rightarrow \infty}\left(3^{n}\right)^{1 / 2 n}\left(\left(\frac{2}{3}\right)^{n}+1\right)^{1 / 2 n}$
Put $\lim _{n \rightarrow \infty} \sqrt{3}$
Put $\lim _{n \rightarrow \infty} \sqrt{3}$
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