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))

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

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

\frac{1}{e}

Decimal Notation

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}

x \to \infty lim (x^{3} + 4)

x \to 0 lim (\frac{x + 6}{x ^{2}})

s \to 1 + lim (\frac{in s}{s - 1})

x \to 0 - lim (x^{2} - \frac{5}{x})

y \to 0 lim (x sin (\frac{1}{y}))

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))