anonymous
  • anonymous
What is a Taylor Series for f(x)=ln(2+2x) ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
ummm I might be able to do this... we'll need to collaborate though
anonymous
  • anonymous
they gave the first part: ln(2)+\[\sum_{n=1}^{\infty}\]
anonymous
  • anonymous
so whats in the sigma, thats important

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anonymous
  • anonymous
thats what we have to try to find lol
anonymous
  • anonymous
does the question say exactly that? What is a taylor series for...
anonymous
  • anonymous
take the derivative of ln(x) like 4 or 5 times see if you can see a pattern
anonymous
  • anonymous
yes, What is a Taylor Series for f(x)=ln(2+2x)
anonymous
  • anonymous
of and at x=1/2 we know that ln(1) = 0
anonymous
  • anonymous
\[\sum_{?}^{?} (f^{(n)}(1/2))/n! * (2x-(1/2))^{n}\]
anonymous
  • anonymous
the general formula would be F^(n) (x) = (-1)^(n+1) (n-1) ! --------------- x^(n)
anonymous
  • anonymous
thats my best guess but I think I'm taking it too fat by kinda approxximating
anonymous
  • anonymous
yes it would now try writing that in sigma notation which is what I did up there...not sure if this is right to do...
anonymous
  • anonymous
>.<
anonymous
  • anonymous
ha, I have no idea
anonymous
  • anonymous
Go to the general form of the Taylor Series. T(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + ... and plug the derivatives of ln(2+2x) into the places you see fit (I think in this case it's safe to set a=0).
anonymous
  • anonymous
I dont know where I would stop using the general form...?
anonymous
  • anonymous
Until you see the general form that they're taking...and then you can put the general form of the series into your sum symbol.

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