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anonymous
 4 years ago
xa<R. I need the detailed explanation of this which is a condition of Taylor Series. Thanks in advance.
anonymous
 4 years ago
xa<R. I need the detailed explanation of this which is a condition of Taylor Series. Thanks in advance.

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0If you have a power series \[ \sum_{n = 0}^\infty a_n (xa)^n\] Via the ratio test, it converges iff \[ \left \frac{a_{n+1} (xa)^{n+1}}{a_n (xa)^n}\right < 1 \] This puts the condition on xa that \[xa < \left \frac{a_n}{a_{n+1}} \right = R\]

cristiann
 4 years ago
Best ResponseYou've already chosen the best response.0xa<R means R<xa<R or R+a<x<R+a In a Taylor series context, a should stand for point around which you discuss the series while R should stand for the radius of the development The theory says that the series (as a function series) uniformly converges on any compact interval [c,d] inside (aR,a+R) and diverges outside (aR, a+R) You have to study for each case the behavior on the boundary, i.e. x=aR and x=a+R The interval (aR, a+R) with the boundaries modified by the above study gives you the convergence domain
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