What is the binomial expansion of #(2 + 3x)^-2#?

1 Answer
cspark1981
Nov 1, 2015

# (2+3x)^(-2) = 1/4(1 - 3x + 27/4x^2 + ...) # when # |x| < 2/3 #

Explanation:

When # |x| < 1 #
# (1+x)^n = 1 + n/(1!)x + (n(n-1))/(2!)x^2 + (n(n-1)(n-2))/(3!)x^3 + ... #

# (2+3x)^(-2) = 1/4(1+3/2x)^(-2) #
# = 1/4(1 - 2 \times 3/2x + 3 \times (3/2x)^2 + ...) # when # |x| < 2/3 #
# = 1/4(1 - 3x + 27/4x^2 + ...) # when # |x| < 2/3 #

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