The positive integer just greater than (1 + 0.0001)^ 10000 is: - Vidyadip

MCQ

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

A
$4$
B
$5$
C
$2$
✓
$3$

✓

Answer

Correct option: D.

$3$

$(1+0.0001)^{10000}$
$=\big(1+\frac{1}{10000}\big)^{10000}$
$=\big(1+\frac{1}{\text{n}}\big)^{\text{n}}=\text{n}\text{c}_{0}(1)^{\text{n}}+\text{n}\text{c}_{1}(1)^{\text{n}-1}\cdot\frac{1}{\text{n}}+\text{n}\text{c}_{2}(1)^{\text{n}-2}\frac{1}{\text{n}^{2}}+\ ....$
$=1+\text{n}\cdot\frac{1}{\text{n}}+\frac{\text{n}(\text{n}-1)}{2}\cdot\frac{1}{\text{n}^2}+\ ....$
$=2+\frac{\text{n}(\text{n}-1)}{2\text{n}^{2}}+\ .... > 2$ Integer just greater than $2$ is $3.$

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