TITLE: Prove that $1+a+a^2+\cdots+a^n=(1-a^{n+1})/(1-a)$.
QUESTION [5 upvotes]: I have problem. Prove this using Mathematical Induction. I am a newbie in Mathematics. Please help me.
$$1+a+a^2+\cdots+a^n = \frac{1-a^{n+1}}{1-a}$$
This is my way for get the proof
Basic Induction:
$$ p(1)= a^1 = 1-a^1+1+1/1-a$$
            $$ = 1-a^3/1-a$$
Really I don't understand this case.

REPLY [2 votes]: For those who don't like induction:
Let $S_n = \sum_{i=0}^{n}a^i$, then $aS_n = \sum_{i=1}^{n+1}a^i$.
So $(1-a)S_n = 1 - a^{n+1}$, the conclusion follows.