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

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

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Answer 1 · 2016-11-04T10:35:46

the answer is $f(x)=1-3x+6x^2-10x^3+15x^4+.....$

Explanation:

The binomial expansion is $(a+b)^n$
$=a^n+na^(n-1)b+(n(n-1))/(1*2)a^(n-2)b^2+.......$

Applying this here with $a=1$ , $b=x$ and $n=-3$
we get
$f(x)=(1+x)^-3=1-3x+((-3)(-4))/(1*2)x^2+((-3)(-4)(-5))/(1*2*3)x^3+((-3)(-4)(-5)(-6))/(1*2*3*4)x^4+......$
$=1-3x+6x^2-10x^3+15x^4+.....$

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

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Explanation:

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

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Explanation:

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