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# Use the binomial series to expand the function f(x)=1(3+x)3 as a power series.?

Use the binomial series to expand the function f(x)=1(3+x)^3 as a power series.

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- kbLv 77 years agoFavorite Answer
Assuming that you mean f(x) = 1/(3 + x)^3:

f(x) = 1/(3 + x)^3

......= 1/(3(1 + x/3))^3

......= (1/27)(1 + x/3)^(-3)

......= (1/27) [1 + (-3)(x/3) + ((-3*-4)/2!) (x/3)^2 + ((-3*-4*-5)/3!) (x/3)^3 + ((-3*-4*-5*-6)/4!) (x/3)^4 + ...]

......= 1/27 - (1/27)x + (2/81) x^2 - (10/729) x^3 + (5/729) x^4 + ...

I hope this helps!

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