# Math Help - Need some help with induction

1. ## Need some help with induction

Hi guys was just wondering if anyone could help me out with this
Use induction to prove
20 + 21 + 22 ... +2n = 2n+1 ​-2

2. ## Re: Need some help with induction

What did you try ?

3. ## Re: Need some help with induction

Presumably you know what "induction" is! First prove the general statement for the specific case n= 0. Is $2^0= 2^{0+1}- 2$?

Then assume it true for some specific (but indeterminate) number, say n= k. That is your "induction hypothesis[/tex] is $2^0+ 2^1+ \cdot\cdot\cdot+ 2^k= 2^{k+1}- 2$. Now you need to use that to show that it is also true when n= k+1. Okay, $2^0+ 2^1+ \cdot\cdot\cdot+ 2^{k+1}= (2^0+ 2^1+ \cdot\cdot\cdot+ 2^k)+ 2^{k+1}$.

Can you apply your induction hypothesis to that?