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Math Help - help with equation in alternate form

  1. #1
    Junior Member
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    May 2009
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    help with equation in alternate form

    I'm told that the following two equations are equal, and asked to write the steps to manipulate the first equation into the second.

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

    to

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

    I've tried many different ways of writing the first equation, but I can't seem to get it to work. Could someone point me in the right direction?
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  2. #2
    Member
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    New Delhi
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    please don't edit your problem if you type something wrong then type it in another post.
    \\edit
    just open brackets
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  3. #3
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    Oct 2009
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    Perhaps it would be easier to show you how to get from the bottom to the top instead of the other way around.
    1 - \frac{1}{(k+1)}  + \frac{1}{(k+1)(k+2)} = 1-\frac{1}{(k+1)} \bigg[1-\frac{1}{(k+2)}\bigg]


    1 - \frac{1}{(k+1)}  + \frac{1}{(k+1)(k+2)} = 1 + \bigg[\bigg(-\frac{1}{(k+1)}*1\bigg) - \bigg(-\frac{1}{(k+1)}*\frac{1}{(k+2)}\bigg)\bigg]


    1 - \frac{1}{(k+1)}  + \frac{1}{(k+1)(k+2)} = 1 + \bigg(-\frac{1}{(k+1)}\bigg) + \bigg(\frac{1}{(k+1)(k+2)}\bigg)

    Does that make it easier? I think the most common error people would make there is not distributing (or removing) the negative along with \frac{1}{(k+1)}.
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  4. #4
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    Thanks so much! That makes sense.
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