Need some help with induction

**vanquishmc** · December 6th 2012, 04:36 AM

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

**Link** · December 6th 2012, 05:06 AM

What did you try ?

**HallsofIvy** · December 6th 2012, 08:26 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, $2^0+ 2^1+ \cdot\cdot\cdot+ 2^{k+1}= (2^0+ 2^1+ \cdot\cdot\cdot+ 2^k)+ 2^{k+1}$ .

Can you apply your induction hypothesis to that?

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