Starting a Taylor series problem, .

[ArcainineFalls531]

Compute the Taylor series for f(x)= sq root (x) about x=1. Determine where the series sconverges absolutely, converges conditionally, and diverges. Hint: 2(k!)=2*4*6...(2k-2)*2k. Also 1<2, 3<4, 5<6,..., 2k-1<2k should help you out with a comparision.

 

[Jameson]

Use Taylor's theorem. $$f(x)=\sum_{n=0}^{\infty}\frac{f^{n}(a)*(x-a)^n}{n!}$$.