# Math Help - Need help with Combinatoric Proof

1. ## Need help with Combinatoric Proof

Hi I need help to find a combinatoric proof regarding :

$2.3^0+2.3^1+...+2.3^{n-1}=3^n -1$

Thanks in advance for the help.

2. Originally Posted by icefirekid
Hi I need help to find a combinatoric proof regarding :

$2.3^0+2.3^1+...+2.3^{n-1}=3^n -1$

Thanks in advance for the help.
I take it that the dots are being used to represent multiplication (though if so they should be written higher, using the command \cdot).

Notice that this is a geometric series, with $a = 2, r = 3$.

So $S_n = \frac{a(r^n - 1)}{r - 1}$

$= \frac{2(3^n - 1)}{3 - 1}$

$= \frac{2(3^n - 1)}{2}$

$= 3^n - 1$.