Limits & Continuity: The lowest integer which is greater than (1+frac110^100 )^10^100 is : | JEE Main 2021 | Yukti Vault

Yukti Vault

JEE Main 2021 (Online) 25th July Evening ShiftQuestion 1

The lowest integer which is greater than $\left(1+\frac{1}{10^{100}}\right)^{10^{100}}$ is :

Limits & Continuity

$1$$2$$3$✓ Correct answer$4$

Solution

$\left(1+\frac1N\right)^N$ is increasing with limit $e$, so $2<\left(1+\frac1N\right)^N<e<3$ for $N=10^{100}$. Lowest integer greater than it is $3$: option C.

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