Find first 4 non zero terms of Power series representation

Question

The first 4 nonzero terms of the power series representation for f(x) = 1/(1+x)3

a. 1-3x+6x² - 6x³

b. 1-3x + 3x² - x³

C. None

d 1-3x + 4x² - 8x³

e. 1-3x + 12x² - 60x³

Answer 1

You can use a MacLaurin series

f(x) ≅ f(0) + x f '(0) + x² f ''(0)/2! + x³ f '''(0)/3!

Alternatively, you can express 1/(1 +x)³ as (1 + x) ^-3 and do a binomial expansion. You'll end up with the same result.

If you need further guidance on how to solve this problem or any other problem in your Calculus course, you can book a session (minimum half hour).

Best wishes.

Hilton

Answer 2

( 1+ x )^-3 = ∑ _n=0^∞ (^-3_n) xⁿ = 1 + (-3)x +[ -3(-3-1) / 2!] x² +[ -3(-3-1)(-3-2) / 3!] x³ +

+[ -3(-3-1)(-3-2)(-3-3) / 4!] x4+.....

Now the ball is in your court