Question

Please Help, Thanks~

Explain how you can use the terms from the binomial expansion to approximate 4.02^5

1st term: 1024
2nd term: 25.6
3rd term: 0.256
4th term: 0.001

Answer 1

Keisha's Response: The 4th term is almost 0, so the 5th and 6th terms are also close to 0. Add the terms shown to approximate 4.025: 1024 + 25.6 + 0.256 + 0.001 = 1049.857.

Explanation:

EDGINUITY

Answer 2

See below. The result using the binomial theorem is 1049.8560 compared with 1049.8573 using a calculator.

Explanation:

Binomial theorem:-

( a + x)^n = a^n + nC1 a^(n-1) x + nC2 a^(n - 2)x^2 + .......

(4 + 0.02)^5 = 4^5 + 5C1* 4^4 *0.02 + 5C2* 4^3* 0.02^2 + 5C3*4^2*0.02^3

+ 5C4 * 4 * 0.02^4 + 0.02^5

= 1024 + 5*4^4*0.02 + 10*4^3*0.02^2 + 10*4^2*0.02^3 + 5*4*0.02^4 + 0.02^5

= 1024 + 25.6 + 0.256 + 0.0000032