It is well known that geometric series are divergent where .
If you must prove it though, since , then we can write .
So
.
Can this limit be evaluted? If so, what does it go to?
basic complex analysis (so z is complex):
Prove that the power series converges at no point on its circle of convergence |z| = 1
Attempt:
I have no idea what to do. This course is driving me nuts. I know for |z| < 1 that series converges to 1/1-z but that is all I know. Can anyone give me a hint?