SOLUTION: Hello I have 3 questions that are all related and I would greatly appreciate it if someone could explain each question step by step in a easy and non complicated way. Thank You

Algebra ->  Finance -> SOLUTION: Hello I have 3 questions that are all related and I would greatly appreciate it if someone could explain each question step by step in a easy and non complicated way. Thank You       Log On


   

Question 1029684: Hello I have 3 questions that are all related and I would greatly appreciate it if someone could explain each question step by step in a easy and non complicated way. Thank You
Use pascal's triangle to write down the binomial expansion of (1+x)⁴ ?
Use the two first terms of the expansion to find an approximate value of (1+0.002)⁴?
Determine the coefficient of x² in the binomial expansion of (1+x)⁴ ?
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Okay...in a prior problem's solution I gave this expansion...we have from Pascal...
1
11
121
1331
14641
as the coefficients (for power n=4) and the expansion is
(1 + x)^4 = 1 + 4x + 6x^2 + 4x^3 + x^4
Notice the powers of x increase from 0 to 4...
(1 + .002)^4 is approximately 1 + 4(.002) = 1.008
The third question is
6(.002)^2 = .000024 and generally insignificant...giving credence to the binomial approximation...