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Math Help - Summation of square root

  1. #1
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    Summation of square root

    Hi all,

    I need a little help with this summation problem.

    Find the value of,

    \sum_{r=1}^4 a_r


    For, a_r = 2 + \sqrt r

    I tried to solve it like this,

    = 2(4) + \sum_{r=1}^4 \sqrt r


    What is the series,

    1, \sqrt 2, \sqrt 3, \sqrt 4, + ....


    Its clearly not a A.P. It also doesn't seem like a G.P. How do I calculate the sum of such a series?

    Thanks for your help.

    P.S. Latex doesn't work anymore. I used QuickLatex to explain the problem.
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  2. #2
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    Isn't it just ?
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  3. #3
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    @Prove It, Thanks for your reply. I realize the no. of terms are small. But I want to learn how to do the summation of square root bit, when I am faced with a similar problem with a larger upper limit
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  4. #4
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    In short, you can't. When all else fails, write each term and simplify.
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  5. #5
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    Quote Originally Posted by Prove It View Post
    In short, you can't.
    Hah! Prove It! Sorry couldn't resist. Thanks.
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  6. #6
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    Quote Originally Posted by Prove It View Post
    Isn't it just ?
    Yes it is.
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