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.
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 $\displaystyle {z(1-z^{n+1})}/(1-z)$ where n->$\displaystyle \infty$. The expression can be expanded to $\displaystyle z/(1-z)+z^{n+2}/(1-z)$ taking the limit n->$\displaystyle \infty$ second term vanishes. That's it!