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Math Help - big equation

  1. #1
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    big equation

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  2. #2
    Senior Member DivideBy0's Avatar
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    You can simplify the LHS by rationalizing the denominator (multiplying by the conjugate over the conjugate and using difference of perfect squares on the bottom to eliminate square roots).

    \frac{1}{\sqrt{n}+\sqrt{n+1}}=\frac{1}{\sqrt{n}+\s  qrt{n+1}} \times \frac{\sqrt{n}-\sqrt{n+1}}{\sqrt{n}-\sqrt{n+1}}=\frac{\sqrt{n}-\sqrt{n+1}}{n-(n+1)}

    =\frac{\sqrt{n}-\sqrt{n+1}}{-1}

    =\sqrt{n+1}-\sqrt{n}

    i.e.

    \frac{1}{\sqrt{4}+\sqrt{5}}=\sqrt{5}-\sqrt{4}

    See if you can use this to solve the problem
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by hotgal24 View Post
    What course is this for?

    You could do this in Excel, or use DivideBy0's hint that this is a telescoping series.

    RonL
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