The Maclaurin Series of an inverse polynomial function

  • #1
Let

[tex]f(x)=\frac{1}{x^2+x+1}[/tex]

Let [itex]f(x)=\sum_{n=0}^{\infty}c_nx^n[/itex] be the Maclaurin series representation for [itex]f(x)[/itex]. Find the value of [itex]c_{36}-c_{37}+c_{38}[/itex].

After working out the fraction, I arrived at the following,

[tex]f(x)=\sum_{n=0}^{\infty}x^{3n}-\sum_{n=0}^{\infty}x^{3n+1}[/tex]

But I dun get how to compare this to the the form given in the question to get the answer...
 

Answers and Replies

  • #2
tiny-tim
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hi kudoushinichi88! :wink:
After working out the fraction

you mean (1-x)/(1 - x3)? :smile:
I arrived at the following,

[tex]f(x)=\sum_{n=0}^{\infty}x^{3n}-\sum_{n=0}^{\infty}x^{3n+1}[/tex]

But I dun get how to compare this to the the form given in the question to get the answer...

but isn't that just c3n = 1, c3n+1 = -1, c3n+2 = 0 ? :confused:
 

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