Anonymous
Anonymous asked in Science & MathematicsMathematics · 7 years ago

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

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

Compute the following coefficients

C0=1

C1=

C2=

C3=

C4=

1 Answer

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  • 7 years ago
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    Binomial expansion:

    (1+x)^n = 1 + nx + n(n-1)/2! x^2 ... + {[n(n-1) ... (n-r+1)]/ [r!]} x^r, where |x| < 1 and x belongs to the set of real values

    so the expansion is...

    1+ 1/3 x + (1/3)(-2/3) / 2! x^2 + (1/3)(-2/3)(-5/3)/3! x^3 + (1/3)(-2/3)(-5/3)(-8/3)/4! x^4...

    C0 = 1

    C1 = 1/3

    C2 = -1/9

    C3 = 5/81

    C4 = -10/243

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