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 $\displaystyle 2^0= 2^{0+1}- 2$?
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?