How do you use the binomial series to expand $f (x) = {(8 + x)}^{\frac{1}{3}}$ $f(x)=(8+x)^(1/3)$ ?

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Answer 1 · 2014-09-22T03:23:55

Since

$(1+x)^{1/3}=sum_{n=0}^infty((1/3),(n))x^n$ ,

by replacting $x$ by 7+x,

$(8+x)^{1/3}=sum_{n=0}^infty((1/3),(n))(7+x)^n$

How do you use the binomial series to expand f(x)=(8+x)^(1/3)f(x)=(8+x)13f(x)=(8+x)^(1/3) ?