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Math Help - Series formula

  1. #1
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    Series formula

    Series formula-assignment-5-question-5-math-1050.png
    Any help with this question would be very much appreciated
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Series formula

    Rationalize the denominator, and you will find you have a telescoping series.
    Thanks from agentmulder
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  3. #3
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    Re: Series formula

    Multiply nominator and denominator by the conjugate expression ( same expression with - sign in the middle) of the denominator....
    the rest is easy as Mark Fl said in his post
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  4. #4
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    Re: Series formula

    I have rationalized the denominator but I don't actually know where to go from there, that is why I am posting this, I don't know the process
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  5. #5
    MHF Contributor MarkFL's Avatar
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    Re: Series formula

    What did you get when you rationalized the denominator?

    If you show your work, then we can better see where you are and how best to help.
    Thanks from agentmulder
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  6. #6
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    Re: Series formula

    sqrt(r+1)-sqrt(r)
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  7. #7
    MHF Contributor MarkFL's Avatar
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    Re: Series formula

    Correct, so we now have:

    \sum_{r=1}^n\left(\sqrt{r+1}-\sqrt{r} \right)=\sum_{r=1}^n\sqrt{r+1}-\sum_{r=1}^n\sqrt{r}

    Now, can you change the index of summation on one of the sums so that you have the same summand in each?
    Thanks from agentmulder
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