$\lim_{n \to \infty} {(1 + \frac{x}{n})}^{n}$

Open in App

Solution

$\lim_{n \to \infty} {(1 + \frac{x}{n})}^{n} = e^{\lim_{n \to \infty} (\frac{x}{n}) \times n} = e^{x}$

Suggest Corrections

Similar questions

Coefficient of $x^{6}$ in $((1 + x) (1 + x^{2})^{2} (1 + x^{3})^{3} . . . . (1 + x^{n})^{n})$ is

\int \frac{d x}{(\sqrt{1 + x^{2}} - x)^{n}} (n \neq \pm 1) = \frac{1}{2} (\frac{z^{n + 1}}{n + 1} + \frac{z^{n - 1}}{n - 1}) + O

x^{8}

(1 + x)^{2} + . . . . . . + (1 + x)^{n} (n \geq 8)

{(1 + x + x^{2} + \cdot \cdot + x^{n})}^{n}

= a_{0} + a_{1} x + a_{2} x^{2} + \cdot \cdot \cdot + a_{m p} x^{m p}

a_{1} + 2 a_{2} + 3 a_{3} + \cdot \cdot \cdot + n p a_{n p}

{(x + 1 + \frac{1}{x})}^{n} (n \in I^{+})

n

Join BYJU'S Learning Program