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Thread: 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.
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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.
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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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