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

3

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

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