Question

Use the first four terms of the binomial theorem to approximate 2.2^7

Answer 1

248.96 which is approximately 249

Explanation:

2.2^7

The coefficients are;

1,7,21,35,35,21,7,1

So the terms we want to use are 1,7,21 and 35

We can write 2.2 as 2+ 0.2

So the approximations are;

1(2)^7(0.2)^0 + 7(2)^6(0.2) + 21(2)^5(0.2)^2 + 35(2)^4(0.2)^3

= 128 + 89.6 + 26.88 + 4.48 = 248.96