# Proof by induction, puzzles by answer

1. Jun 6, 2012

Ok, so there's this proof by induction question. I looked at the answer for it but I don't understand it.

How does it get from being 2^(k+1) to being 2^(k+2)?

Last edited by a moderator: Jun 6, 2012
2. Jun 6, 2012

You need to provide a little more background into your question, I think.

3. Jun 6, 2012

4. Jun 6, 2012

### D H

Staff Emeritus
$2^{k+1}(k-1+k+1) = 2^{k+1}(2k) = 2^{k+2}k$

5. Jun 11, 2012

### rustynail

you got [2^(k+1)](2k).

multiply 2^(k+1) by two, that is raising your exponent by 1. Hence 2^(k+2)

Last edited: Jun 11, 2012