For the power series of the form, $∑_{i=0}^∞ a_i z^i,$ which one of the following may not be true?

Question

TuteeHUB · Accepted Answer

NA

TuteeHUB · Answer

The series converges only for z=0

TuteeHUB · Answer

The series converges absolutely for all z

TuteeHUB · Answer

The series converges absolutely for all z in some finite open interval (-R, R) and diverges if zR

TuteeHUB · Answer

At the points z=R and z=-R, the series will diverge

1.	For the power series of the form, \(∑_{i=0}^∞ a_i z^i,\) which one of the following may not be true?
A.	The series converges only for z=0
B.	The series converges absolutely for all z
C.	The series converges absolutely for all z in some finite open interval (-R, R) and diverges if z<-R or z>R
D.	At the points z=R and z=-R, the series will diverge
Answer» E.

For the power series of the form, \(∑_{i=0}^∞ a_i z^i,\) which one of the following may not be true?