# How do you use the binomial theorem to approximate (2.005)^10?

Feb 20, 2017

$\approx 1049.6$

#### Explanation:

${\left(2.005\right)}^{10}$

$= {2}^{10} {\left(1.0025\right)}^{10}$

$= 1024 {\left(1 + 0.0025\right)}^{10}$

$= 1024 \left(1 + \left(10\right) 0.0025 + \setminus O \left({0.0025}^{2}\right)\right)$

$\approx 1049.6$