What is the limit as n approaches infinity of (1-3/n)^{2n} ?

The limit as n approaches infinity of (1-3/n)^{2n} is 1/(e^6)

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limit as n approaches infinity of (1-3/n)^{2n}

n \to \infty lim ((1 - \frac{3}{n})^{2 n})

\frac{1}{e ^{6}}

Decimal

0.00247 \dots

Solution steps

n \to \infty lim ((1 - \frac{3}{n})^{2 n})

Apply exponent rules

= n \to \infty lim (e^{2 n l n (1 - \frac{3}{n})})

Apply the Limit Chain Rule:

\frac{1}{e ^{6}}

= \frac{1}{e ^{6}}

What is the limit as n approaches infinity of (1-3/n)^{2n} ?
The limit as n approaches infinity of (1-3/n)^{2n} is 1/(e^6)