Hi guys was just wondering if anyone could help me out with this

Use induction to prove

2^{0 }+ 2^{1 }+ 2^{2 }... +2^{n }= 2^{n+1 }-2

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- Dec 6th 2012, 04:36 AMvanquishmcNeed some help with induction
Hi guys was just wondering if anyone could help me out with this

Use induction to prove

2^{0 }+ 2^{1 }+ 2^{2 }... +2^{n }= 2^{n+1 }-2 - Dec 6th 2012, 05:06 AMLinkRe: Need some help with induction
What did you try ?

- Dec 6th 2012, 08:26 AMHallsofIvyRe: Need some help with induction
Presumably you know what "induction" is! First prove the general statement for the specific case n= 0. Is $\displaystyle 2^0= 2^{0+1}- 2$?

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

Can you apply your induction hypothesis to that?