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Math Help - [SOLVED] algebra in P.M.I

  1. #1
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    [SOLVED] algebra in P.M.I

    I am still having trouble following the simplification of equations in the Induction examples i am studying.
    The notes I have use this:

    <br />
[\frac{1}{2}k(k+1)] + (k+1)<br />
    which is simplified to
    <br />
\frac{1}{2}(k+1)[(k+1)+1]<br />

    but when I do the math I get
    <br />
[\frac{1}{2}k(k+1)] + (k+1) = [\frac{1}{2}k^2 + k] + (k+1) = [\frac{1}{2}k^2 + k] + (k+1)<br />

    so if anyone could explain the steps used in the former expression I would me much appreciative
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  2. #2
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    Quote Originally Posted by dunsta View Post
    I am still having trouble following the simplification of equations in the Induction examples i am studying.
    The notes I have use this:

    <br />
[\frac{1}{2}k(k+1)] + (k+1)<br />
    which is simplified to
    <br />
\frac{1}{2}(k+1)[(k+1)+1]<br />

    but when I do the math I get
    <br />
[\frac{1}{2}k(k+1)] + (k+1) = [\frac{1}{2}k^2 + k] + (k+1) = [\frac{1}{2}k^2 + k] + (k+1)<br />

    so if anyone could explain the steps used in the former expression I would me much appreciative

    [\frac{1}{2}k(k+1)] + (k+1)

    Factor out (k+1)

    (k+1)(1+\frac{1}{2}k)

    You can get a 1/2 on the outside by multiplying by 1 = (1/2)(2)

    \frac{1}{2}(k+1)(2+k)

    <br />
\frac{1}{2}(k+1)[(k+1)+1]<br />
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  3. #3
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    I am getting there slowly, thanks. I am sorry for my ignorance.

    I know what factoring is, but could you explain the first step of how to factor out
    [\frac{1}{2}k(k+1)] + (k+1)<br />

    in more detail please?
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  4. #4
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    Quote Originally Posted by dunsta View Post
    I am getting there slowly, thanks. I am sorry for my ignorance.

    I know what factoring is, but could you explain the first step of how to factor out
    [\frac{1}{2}k(k+1)] + (k+1)<br />

    in more detail please?
    Sure. We have two terms (addends) that are both divisible by (k+1).

    Maybe imagine it like this

    ab + b = b(a + 1)

    where a = \frac{1}{2}k and b = k+1.
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  5. #5
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    Ok, got it, just needed to refresh my brain of some basic algebra!!


    Thanks, I understand the expression, but I still can't see how to divide

    [\frac{1}{2}k(k+1)] + (k+1)<br />

    by (k+1)
    Last edited by dunsta; June 9th 2010 at 06:43 AM. Reason: figured it out :)
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