anonymous
  • anonymous
Taylor series picture #12
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
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anonymous
  • anonymous
i came up with \[\sum_{0}^{\infty} -(x+2)^n\]
anonymous
  • anonymous
first one you want to expand about 1 so it should look like \[f(1)+f'(1)(x-1)+\frac{f''(1)}{2}(x-1)^2+\frac{f'''(1)}{3!}(x-1)^3+...\]

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anonymous
  • anonymous
\[f(1)=\frac{1}{2}\] \[f'(x)=-\frac{1}{(1+x)^2}\] \[f'(1)=-\frac{1}{4}\] etc a nice patter will emerge
anonymous
  • anonymous
ok i'll give it a try
anonymous
  • anonymous
why is it (x-1)?
anonymous
  • anonymous
its centered at c=-2 so i thought it would be (x+2)
anonymous
  • anonymous
we can take the derivatives for the first one easily \[f'(x)=-(x+1)^{-2}\] \[f''(x)=2(x+1)^{-3}\] \[f'''(x)=-6(x+1)^{-4}\] etc
anonymous
  • anonymous
oh i was doing the wrong one sorry
anonymous
  • anonymous
yes the second one should be in powers of (x+2)
anonymous
  • anonymous
that one is much easier, and now that i look i see you have the answer, so ignore what i wrote
anonymous
  • anonymous
how do i find the radius of convergence?
anonymous
  • anonymous
i did limit as n-> infinity abs(a_n+1/a_n)

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