# Need some help with induction

• December 6th 2012, 04:36 AM
vanquishmc
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
• December 6th 2012, 05:06 AM
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, $2^0+ 2^1+ \cdot\cdot\cdot+ 2^{k+1}= (2^0+ 2^1+ \cdot\cdot\cdot+ 2^k)+ 2^{k+1}$.