The positive integer just greater than (1 + 0 | vedclass

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Question

(D) We know that $e = \lim_{n 	o \infty} (1 + \frac{1}{n})^n$ and $2 < e < 3$.For $n = 10000$,the expression $(1 + \frac{1}{10000})^{10000} = (1 + 0.

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(D) We know that $e = \lim_{n 	o \infty} (1 + \frac{1}{n})^n$ and $2 For $n = 10000$,the expression $(1 + \frac{1}{10000})^{10000} = (1 + 0.0001)^{10000}$.Since the sequence $(1 + \frac{1}{n})^n$ is strictly increasing and approaches $e$ from below,we have $(1 + 0.0001)^{10000} Using the binomial expansion,$(1 + 0.0001)^{10000} = 1 + 10000(0.0001) + \frac{10000 	imes 9999}{2!} (0.0001)^2 + \dots = 1 + 1 + \frac{0.9999}{2} + \dots > 2$.Thus,$2 The positive integer just greater than $(1 + 0.0001)^{10000}$ is $3$.Therefore,the correct option is $D$.

The positive integer just greater than $(1 + 0.0001)^{10000}$ is

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