What is the value of $\sum_{n=0}^\infty i^n$?

Question

Is $\sum_{n=0}^\infty i^n=\frac{1}{1-i}$?

$|i|=1$. Is this series convergent?

Answer 1

The series clearly is not convergent, because the terms do not tend to $0$.

Answer 2

No the series does not converge according to the divergence test.

The answer that you have provided is not valid.

Answer 3

No, it is not convergent. Note that the terms cycle through $1,i,-1,-i,1,i,-1,-i\ldots$ so the sum oscillates through four values as well. You are on the circle of convergence of the geometric series where convergence is not guaranteed.