The correct option is B e^3 We have, lim_n→∞ (1+3n)^n We know that lim_x→∞ (1+px)^x=e^p Therefore, lim_n→∞ (1+3n)^n =e^3 Hence, this is th ...

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Rationalization Method to Remove Indeterminate Form

Solve: limn→...

Question

Solve:
${lim}_{n \to \infty} {(1 + \frac{3}{n})}^{n}$

e

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e^{3}

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e^{0} = 1

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e^{2}

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Solution

The correct option is B $e^{3}$
We have,
${lim}_{n \to \infty} {(1 + \frac{3}{n})}^{n}$

We know that
${lim}_{x \to \infty} {(1 + \frac{p}{x})}^{x} = e^{p}$

Therefore,
${lim}_{n \to \infty} {(1 + \frac{3}{n})}^{n}$
$= e^{3}$

Hence, this is the answer.

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