idku
  • idku
tell me if I am doing this correctly. I haven't touched math for a while now.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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idku
  • idku
(I am just reviewing some concepts from the past) I want to find the power series representation for \(\displaystyle\large\color{black}{\tan^{-1}(x)}\) now I will show my work....
idku
  • idku
\(\displaystyle\large\color{black}{\frac{1}{1-x}=\sum_{n=0}^{\infty}x^n}\) \(\displaystyle\large\color{black}{\frac{1}{1+x}=\sum_{n=0}^{\infty}(-1)^nx^n}\) \(\displaystyle\large\color{black}{\frac{1}{1+x^2}=\sum_{n=0}^{\infty}(-1)^nx^{2n}}\) \(\displaystyle\large\color{black}{\int \frac{1}{1+x^2}~dx~=~\int~\sum_{n=0}^{\infty}(-1)^nx^{2n}~dx}\) \(\displaystyle\large\color{black}{\tan^{-1}(x)~=~\sum_{n=0}^{\infty}\frac{(-1)^nx^{2n}}{2n+1}}\)
idku
  • idku
and I am not placing +C, because I am looking for specific function - representation and not a family of functions.

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idku
  • idku
oh my power is off
idku
  • idku
\(\displaystyle\large\color{black}{\tan^{-1}(x)~=~\sum_{n=0}^{\infty}\frac{(-1)^nx^{2n+1}}{2n+1}}\)
idku
  • idku
this should be correct, if I didn't err anywhere once again.
geerky42
  • geerky42
What's the problem here? You already represented \(\tan^{-1}(x)\) as series in your other question here.
idku
  • idku
yeah forgot about that..... my apologies.
idku
  • idku
tnx for the confirmation, and bye:)
geerky42
  • geerky42
Ok no problem.

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