Taylor series with summation notation

  • #1

Homework Statement



f(x) = [tex]\frac{1-cos(X^2)}{x^3}[/tex]

which identity shoud i use?
and tips on this type of questions? once i can separate them, then i'll be good


thanks!
 

Answers and Replies

  • #2
benorin
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Do you know a Taylor series for [itex]\cos x[/itex]?
 
  • #3
Do you know a Taylor series for [itex]\cos x[/itex]?

yeah, but there's a x^3 on the bottom...
 
  • #4
Cyosis
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Sure, but the summation isn't over x so you can put the x in the sum or outside the sum.
 
  • #5
benorin
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Example:

[tex]\frac{1-\sin 2x^3}{x}=\frac{1-\sum_{k=0}^{\infty}\frac{\left( 2x^3\right)^{2k+1}}{(2k+1)!}}{x} = {\scriptstyle \frac{1}{x}}-{\scriptstyle \frac{1}{x}}\sum_{k=0}^{\infty}\frac{2^{2k-1}x^{6k+3}}{(2k+1)!}[/tex]
= {\scriptstyle \frac{1}{x}}-\sum_{k=0}^{\infty}\frac{2^{2k-1}x^{6k+2}}{(2k+1)!}[/tex]​
 

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