What is the limit as k approaches infinity of (1-1/(2k))^k ?

The limit as k approaches infinity of (1-1/(2k))^k is 1/(sqrt(e))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as k approaches infinity of (1-1/(2k))^k

k \to \infty lim ((1 - \frac{1}{2 k})^{k})

\frac{1}{e}

Decimal

0.60653 \dots

Solution steps

k \to \infty lim ((1 - \frac{1}{2 k})^{k})

Apply exponent rules

= k \to \infty lim (e^{k l n (1 - \frac{1}{2 k})})

Apply the Limit Chain Rule:

\frac{1}{e}

= \frac{1}{e}

What is the limit as k approaches infinity of (1-1/(2k))^k ?
The limit as k approaches infinity of (1-1/(2k))^k is 1/(sqrt(e))