# Thread: Confusion in Inductive Proofs

1. ## Confusion in Inductive Proofs

Hey guys, I've been lurking around this site for a while, but I decided to finally stick in a question. Well, two, but I'll post one first and see if I can figure out the next one with the advice or help I get.

I will post the question and then my working out and then what I'm confused about, just to keep it clear and concise.
The Question:

My Working Out:

however, shouldn't I get an answer like

or something rather than a 2^(2k + 1 + 1) -2

Hopefully I didn't make it too messy or make a silly mistake.
Thanks.

2. ## Re: Confusion in Inductive Proofs

Originally Posted by ACARROT
Hey guys, I've been lurking around this site for a while, but I decided to finally stick in a question. Well, two, but I'll post one first and see if I can figure out the next one with the advice or help I get.

I will post the question and then my working out and then what I'm confused about, just to keep it clear and concise.
The Question:
.
Here is what you are missing.
\begin{align*}2^{k+1}-2+2^{k+1}&=2^{k+1}+2^{k+1}-2 \\&=2^{k+1}(1+1)-2\\&=2^{k+1}(2)-2\\&=2^{k+2}-2 \end{align*}
QED

3. ## Re: Confusion in Inductive Proofs

Ohhhhh I think I get it! You turn it into

(2^(k+1)) * (2^1)) - 2

which due to index laws state that it becomes (2^(k + 1 + 1)) - 2!

In a simpler format:

Thanks!