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$\displaystyle\sum_{i=0}^n2^i=2^{n+1}-1$.

I don't understand induction so I could use some help.

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    @Paul, could you fix your edit, as you forgot the $2^i$ on the left.2012-03-24
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    @Pjennings: Oh, sorry. But someone fixed it already.2012-03-24
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    See [this answer](http://math.stackexchange.com/a/180255/15941) to a [similar question](http://math.stackexchange.com/q/180169/15941) that did not insist on a proof via induction.2012-08-30
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    This is a very similar question, too: [Prove by induction that $2^1+2^2+2^3+2^4+ \cdots +2^n=2(2^n-1)$](http://math.stackexchange.com/questions/88132/prove-by-induction-that-21222324-cdots-2n-22n-1). (And you can also check the questions linked to that one.)2012-08-30

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