Question

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

Answer 1

`approx 1049.6`

Explanation:

`(2.005)^10`

`= 2^10 (1.0025)^10`

`= 1024 (1 + 0.0025)^10`

`= 1024 (1 + (10)0.0025 + \O(0.0025^2) )`

`approx 1049.6`