Binomial Theorem — MATHS STD 11 Science — Question

4. 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.