Official PYQ · 2010Q5Calculus: Limits, Continuity, DifferentiabilityMCQ1 mark

GATE CS 2010 Q5 — Calculus: Limits, Continuity, Differentiability

What is the value of $\displaystyle\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{2n}$ ?

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Answer: B

We need to find the limit:

$\lim_{n \to \infty} \left(1 - \frac{1}{n}\right)^{2n}$

Using the standard limit identity $\lim_{n \to \infty} \left(1 + \frac{x}{n}\right)^n = e^x$ , we can rewrite the expression as:

$\left[ \lim_{n \to \infty} \left(1 - \frac{1}{n}\right)^n \right]^2$

Substituting $x = -1$ into the identity gives:

$\lim_{n \to \infty} \left(1 - \frac{1}{n}\right)^n = e^{-1}$

Therefore, the limit is:

$(e^{-1})^2 = e^{-2}$

Thus, the correct option is B.

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Published 10 Oct 2026

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