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

JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Limits

The lowest integer which is greater than

(1 + \frac{1}{1 0 ^{100}})^{1 0^{100}}

is .........

Answer: (A)

The sequence

a_{n} = (1 + \frac{1}{n})^{n}

increases with

n

and converges to

e

, so for every

n > 1

2 = a_{1} < a_{n} < e < 3

With

n = 1 0^{100}

the value lies strictly between

2

and

3

, so the lowest integer greater than it is

3

JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Single correct option

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