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  1. #1
    RAz
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    Mathematical proof help

    Proofs seem to be my weakest point when it comes to math. My teacher says that it is like an art form...one that will take me a very long time to understand.

    Here is my question:

    Prove the following by induction, where n is a positive integer.

    1+2+3+4+....+ 2^(2-1) = 2^n - 1

    My knowledge of proofs is very basic. I can only do things like "prove root3 is irrational" etc. I have trouble with them becasue there is no solid set of formulas you can use.
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  2. #2
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    are you sure it is:

    1+2+3+4+...+2^(2-1)?

    THis would be 1+2+3+4+...+2
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  3. #3
    RAz
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    Quote Originally Posted by jzellt View Post
    are you sure it is:

    1+2+3+4+...+2^(2-1)?

    THis would be 1+2+3+4+...+2
    My mistake. It is 2^(n-1).
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  4. #4
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    Quote Originally Posted by RAz View Post
    Proofs seem to be my weakest point when it comes to math. My teacher says that it is like an art form...one that will take me a very long time to understand.

    Here is my question:

    Prove the following by induction, where n is a positive integer.

    1+2+3+4+....+ 2^(2-1) = 2^n - 1

    My knowledge of proofs is very basic. I can only do things like "prove root3 is irrational" etc. I have trouble with them becasue there is no solid set of formulas you can use.
    Quote Originally Posted by RAz View Post
    My mistake. It is 2^(n-1).
    If that's the case, then surely the series is 1 + 2 + 4 + \cdots + 2^{n-1}, NOT 1 + 2 {\color{red}+ 3} + 4 + \cdots + 2^{n-1}.

    Please take greater care with what you post.

    Are you familiar with the three steps in proof by induction? Where do you get stuck in this process?

    A hint for step 3: (2^k - 1) + 2^k = 2 \cdot 2^k - 1 = 2^{k+1} - 1.
    Last edited by mr fantastic; February 18th 2009 at 01:47 AM.
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