How to write this in series form? Watch

Shadow!
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#1
Report Thread starter 9 years ago
#1
Hey, if |x|<1, how do I write:

\frac{1}{(1+x)^2}

in a power series form? [summation form]

I wrote it in summation form for \frac{1}{(1+x)} and combined summations, but I'm not sure if that's right.

Thanks.
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ghostwalker
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#2
Report 9 years ago
#2
(Original post by Shadow!)
Hey, if |x|<1, how do I write:

\frac{1}{(1+x)^2}

in a power series form? [summation form]

I wrote it in summation form for \frac{1}{(1+x)} and combined summations, but I'm not sure if that's right.

Thanks.
You should be familiar with the binomial expansion.

\frac{1}{(1+x)^2} is just (1+x)^{-2}
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miml
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Notice that  \dfrac{1}{(1+x)^2} = \dfrac{d}{dx}\dfrac{-1}{x+1} .

Can you see where to go from there?
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Shadow!
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(Original post by ghostwalker)
You should be familiar with the binomial expansion.

\frac{1}{(1+x)^2} is just (1+x)^{-2}
Does this bring in combinations/binomial coefficients though? Is there a way to write it without them?
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ghostwalker
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(Original post by Shadow!)
Does this bring in combinations/binomial coefficients though? Is there a way to write it without them?
The other way is as miml said.
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rbnphlp
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(Original post by ghostwalker)
The other way is as miml said.
probably being stupid , why cant you use taylor/mclaurian series here ?
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ghostwalker
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(Original post by rbnphlp)
probably being stupid , why cant you use taylor/mclaurian series here ?
Could do.

OP. There you go, three possibilities.
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