How do you use the binomial series to expand #1 / (1+x)^4#?
1 Answer
Feb 1, 2016
# 1 - 4x +10x^2 - 20x^3 + 35x^4 +......#
Explanation:
rewrite as
# (1+x)^-4 #
Since there is a negative exponent use the following version
of the binomial expansion.
#(1 + x)^n≣ 1+nx+(n(n-1))/(2!) x^2 + (n(n-1)(n-2))/(3!) x^3 +..# (here n = -4 )
#1 +(-4)x+((-4)(-5))/(2!) x^2+((-4)(-5)(-6))/(3!) x^3 + ...#
# = 1 -4x +(20)/2 x^2 -(120)/6 x^3 + ...#
# rArr(1+x)^-4 ≣ 1 - 4x + 10x^2 -20x^3 + 35x^4 +....#
