Question

Which number is larger ${\left(1.01\right)}^{1000000}$ or $10,000?$

Answer 1

By Binomial Theorem
${\left(1.01\right)}^{1000000}={(1+0.01)}^{1000000}$
$=1{+}^{1000000}{\text{C}}_1\left(0.01\right)+$ other positive terms
$=1+1000000\times 0.01+$ other positive terms
$=1+10000+$ other positive terms
Hence, ${\left(1.01\right)}^{1000000}>10,000$