Proof of convergence of a geometric power series

Question

While reading a time series analysis textebook I've stumbled upon an assertion which I struggle to understand.

If $|a|<1$ then $1 + a+ a^2 + a^3 + ... + a^n$ converges to $\frac{1}{1-a}$ as $n$ approaches infinity.

A reference to a clear proof would be highly appreciated.

Answer 1

I found this one to be pretty straight forward: http://mathfaculty.fullerton.edu/mathews/c2003/complexgeometricseries/ComplexGeometricSeriesTheorem.1.pdf