Using binomial theorem determine which number is larger (1.2)

We have:

$(1.2)^{4000}=(1+0.2)^{4000}$

$={ }^{4000} C_{0}+{ }^{4000} C_{1} \times(0.2)^{1}+{ }^{4000} C_{2} \times(0.2)^{2}+\ldots{ }^{4000} C_{4000} \times(0.2)^{4000}$

$=1+4000 \times 0.2+$ other positive terms

$=1+800+$ other positive terms

$=801+$ other positive terms

$\because 801>800$

Hence, (1.2)4000 is greater than 800