- #1
jacobrhcp
- 169
- 0
Homework Statement
Prove that the radius of convergence [tex]\rho[/tex] of the power series [tex]\sum[/tex]ck (z-a)^k over all k, equals 1/R when ck is not 0 and you know that:
|[tex]\frac{ck+1}{ck}[/tex]|=R>0
Homework Equations
I was planning on using that the radius of convergence is in this case:
[tex]\rho[/tex]= 1/limsup(|ck|^1/k) ( and k->infinity)
The Attempt at a Solution
I tried to make it sensible that
limsup(|ck|^1/k)=|[tex]\frac{ck+1}{ck}[/tex]|=R
I've been staring at it for quite some hours now (it's 3 in the morning and it's got to be done by 9 o'clock this morning... so any help would be greatly appreciated, though I understand if you think it's my own fault)
Last edited: