Anonymous
Anonymous asked in Science & MathematicsMathematics · 7 years ago

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.

c0-c4

1 Answer

Relevance
  • kb
    Lv 7
    7 years ago
    Favorite 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!

Still have questions? Get your answers by asking now.