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Return to GATE2010 q5.
What is the value of $\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{2n}$ ?
(A) 0
(B) $e^{-2}$
(C) $e^{-1/2}$
(D) 1
We know that $\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{n} = e^{-1}$, so $$\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{2n} = e^{-2}$$. So, option (B) is correct.
GATECSE