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
Presumably you know what "induction" is! First prove the general statement for the specific case n= 0. Is ?
Then assume it true for some specific (but indeterminate) number, say n= k. That is your "induction hypothesis[/tex] is . Now you need to use that to show that it is also true when n= k+1. Okay, .
Can you apply your induction hypothesis to that?