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Thread: Confusion in Inductive Proofs

  1. #1
    Newbie ACARROT's Avatar
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    Unhappy 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:
    Confusion in Inductive Proofs-screen-shot-2017-07-05-3.04.43-pm.png
    My Working Out:

    Confusion in Inductive Proofs-screen-shot-2017-07-05-3.11.54-pm.png
    however, shouldn't I get an answer like
    Confusion in Inductive Proofs-screen-shot-2017-07-05-3.13.04-pm.png
    or something rather than a 2^(2k + 1 + 1) -2

    Hopefully I didn't make it too messy or make a silly mistake.
    Thanks.
    Attached Thumbnails Attached Thumbnails Confusion in Inductive Proofs-screen-shot-2017-07-05-3.03.07-pm.png  
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  2. #2
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    Re: Confusion in Inductive Proofs

    Quote Originally Posted by ACARROT View Post
    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:
    Click image for larger version. 

Name:	Screen Shot 2017-07-05 at 3.04.43 PM.png 
Views:	4 
Size:	37.1 KB 
ID:	37846.
    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
    Thanks from ACARROT
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  3. #3
    Newbie ACARROT's Avatar
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    Wink 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:
    Confusion in Inductive Proofs-screen-shot-2017-07-05-4.48.29-pm.png

    Thanks!
    Last edited by ACARROT; Jul 4th 2017 at 08:49 PM.
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