Thread: [SOLVED] Complex Analysis: Limits!!!

What is the limit and n tends to infintity of
z+z^2+z^3+...+z^n
note z belongs to the complex plane and is defined on the disc with centre 0 and radius 1.

I think it should be 1/(1-z) but I cant see why.

Thanks

Originally Posted by syster

What is the limit and n tends to infintity of
z+z^2+z^3+...+z^n
note z belongs to the complex plane and is defined on the disc with centre 0 and radius 1.

I think it should be 1/(1-z) but I cant see why.

Thanks

use this fact: the sum is equal to where n-> . The expression can be expanded to taking the limit n-> second term vanishes. That's it!