Question

Using Binomial Theorem, indicate which number is larger $(1.1)^{10000}$ or $1000.$

Answer 1

By splitting $1.1$ and then applying Binomial Theorem, the first few terms of $(1.1)^{10000}$ can be obtained as

$(1.1) ^{10000} = (1+0.1)^{ 10000}$
=$^{10000}C_0 + ^{10000}C_1(1.1)\,+\,\text{Other positive terms}$
=$1+10000×1.1+ \text{Other positive terms }$
=$1+11000+\text{Other positive terms}$
$> 1000$

$\text{Hence,}\, (1.1)^{10000} >1000$.