Adding decreasing power of the same number

Question

Simpler ways of writing for example $a^{n}$ + $a^{n-1}$ + $a^ {n-2}$ + ... + a=

what is this even called ?

Answer 1

This is a (finite) geometric series, which can be given by the formula $$ \sum_{k=0}^{n}a^k= \frac{a(1-a^n)}{1-a} \, . $$