832/VB03. problem / Math - Solved Math Problems

MR-832 / 1503. problem

Determine the limit value of the series:

$a_{n} = {(1 + \frac{3}{n})}^{n}$

$\underset{n \to \infty}{l i m} {(1 + \frac{3}{n})}^{n}$

$\frac{3}{n} = \frac{1}{t}$

$3 \cdot t = n$

$\begin{matrix} n \to \infty \\ t \to \infty \end{matrix}$

$\underset{t \to \infty}{l i m} {(1 + \frac{1}{t})}^{3 \cdot t}$

$= \underset{t \to \infty}{l i m} {[{(1 + \frac{1}{t})}^{t}]}^{3}$

$= {[\underset{t \to \infty}{l i m} {(1 + \frac{1}{t})}^{t}]}^{3}$

$= e^{3}$

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