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I have this problem:

What is the Taylor series of $\sqrt{x}$ at $x_0 = 4$. What is its interval of convergence?

I am stuck and I can not finish it.

Any idea on how to do that?

Thank you

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  • $\begingroup$ What have you done so far? $\endgroup$ – Aretino Dec 2 '15 at 22:28
  • $\begingroup$ @Aretino nothing important, just small tests that do not conclude to a final result. $\endgroup$ – zeeks Dec 2 '15 at 22:37
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    $\begingroup$ If you know the answer for $\sqrt{1+t}$ at $0$, write $x=x_0+h=4+h$, and deal with $\sqrt{4+h} = 2\sqrt{1+h/4}$ instead. $\endgroup$ – Clement C. Dec 2 '15 at 22:39

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