Is it possible for radius of convergence to be negative?

[jkh4]

is it possible for "R" (radius of convergence) to be negative?

is it possible for "R" (radius of convergence) to be negative?

for example: -|x|<1 and R=-1?

 

[Hurkyl]

What does the definition say?

 

[Office_Shredder]

is it possible for "R" (radius of convergence) to be negative?

for example: -|x|<1 and R=-1?

If -|x|< 1,then x can be any number. So it's not a very useful thing to say

 

[HallsofIvy]

As Hurkyl said, take any Calculus book and look up the definition of "radius of convergence"!