# Using binomial theorem, indicate which is larger (1.1)

Question:

Using binomial theorem, indicate which is larger (1.1)10000 or 1000.

Solution:

We have:

(1.1)10000

$=(1+0.1)^{10000}$

$={ }^{10000} C_{0} \times(0.1)^{0}+{ }^{10000} C_{1} \times(0.1)^{1}+{ }^{10000} C_{2} \times(0.1)^{2}+\ldots{ }^{10000} C_{10000} \times(0.1)^{10000}$

$=1+10000 \times 0.1+$ other positive terms

$=1+10000+$ other positive terms

$=10001+$ other positive terms

$\because 10001>1000$

$\therefore(1.1)^{10000}>1000$