anonymous
  • anonymous
So I have this function: \[f(x)=(1+x)^{-3}\] And I need to find the Maclaurin's serie. I have found the following: \[=f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)x^2}{2!}+...\] \[=1-\frac{3x}{1!}+\frac{12x^2}{2!}-\frac{60x^3}{3!}+...\] How do I convert this to a Sum?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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SolomonZelman
  • SolomonZelman
I will rely on your result, \(\large\color{#000000 }{ \displaystyle \sum_{k=0}^{\infty} \frac{}{k!}}\) but up to here it is fairly obvious if you look at the denominators, and recall also that 0!=1.
SolomonZelman
  • SolomonZelman
Something happened to the equation in your question, but I can still read it...
SolomonZelman
  • SolomonZelman
wait, is there a reason you removed it? you think it's incorrect?

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anonymous
  • anonymous
I havent removed anything?
SolomonZelman
  • SolomonZelman
oh you didn't remove it and my latex is just not readin
anonymous
  • anonymous
I think it is bugging. But I wrote: So I have this function: \[f(x)=(1+x)^{-3}\] And I need to find the Maclaurin's serie. I have found the following: \[=f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)x^2}{2!}+...\] \[=1-\frac{3x}{1!}+\frac{12x^2}{2!}-\frac{60x^3}{3!}+...\] How do I convert this to a Sum?
anonymous
  • anonymous
Yea, so I am having trouble finding the nominator.
SolomonZelman
  • SolomonZelman
I missed it, I will erase the mess I made.
anonymous
  • anonymous
\[\sum_{k=0}^{\infty}(-1)^k \frac{ (k+1)(k+2) }{ 2 }\]
anonymous
  • anonymous
Wouldnt that make sense?
anonymous
  • anonymous
missed \[x^n\] at the end
anonymous
  • anonymous
\[\sum_{k=0}^{\infty}(-1)^k \frac{ (k+1)(k+2) }{ 2 }x^k\]
SolomonZelman
  • SolomonZelman
and without k! ?
anonymous
  • anonymous
Yea, but maybe this isnt a maclaurins serie?
SolomonZelman
  • SolomonZelman
I will see if I can redo it and rethink it...
SolomonZelman
  • SolomonZelman
I am lagging I need more time because that; apologize.
anonymous
  • anonymous
Dont worry
SolomonZelman
  • SolomonZelman
I am lagging so bad I am sorry
anonymous
  • anonymous
No worries, ill take a look at some other questions. Thanks for your help though :)
SolomonZelman
  • SolomonZelman
\[\sum_{k=0}^{\infty}(-1)^k \frac{ (k+1)(k+2) }{ 2 }x^k\] was correct
SolomonZelman
  • SolomonZelman
Sorry for wasting your time.... (a bit frusturating with this internet. I got to go offline)
anonymous
  • anonymous
No worries, have a great day

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