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Math Help - Series and sequences

  1. #1
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    Series and sequences

    Can somebody teach me how to solve this question? Please…

    Sorry... since i don't know how to write the symbols here... so i used attachment...
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  2. #2
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    Re: Series and sequences

    Quote Originally Posted by AuXian View Post
    Show that \sum_{n=1}^r\frac{r^2+r^{-1}}{r^2+r}=\frac{n^2}{n+1}
    So, are you summing r constants (i.e., expressions that don't depend on n)?
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  3. #3
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    Re: Series and sequences

    If it's \sum_{r = 1}^n \frac{r^2 + r^{-1}}{r^2 + r} = \frac{n^2}{n+1}, then it isn't even true.

    n =1: LHS = \frac{1^2 +1^{-1}}{1^2 + 1} = \frac{2}{2} = 1. RHS = \frac{1^2}{1+1} = \frac{1}{2}.

    n =2: LHS = (1) + \frac{2^2 +2^{-1}}{2^2 + 2} = 1 + \frac{4.5}{6} = \frac{7}{4}. RHS = \frac{2^2}{2+1} = \frac{4}{3}.
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  4. #4
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    Re: Series and sequences

    Quote Originally Posted by emakarov View Post
    So, are you summing r constants (i.e., expressions that don't depend on n)?
    ya... only the final step will convert r to n... It is needed to show that LHS=RHS, the LHS will be used. My problem is, I don't know how to simplify the earlier part (about r)...
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  5. #5
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    Re: Series and sequences

    Quote Originally Posted by AuXian View Post
    only the final step will convert r to n...
    I am not sure what this means. Please write the question correctly.
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  6. #6
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    Re: Series and sequences

    Quote Originally Posted by emakarov View Post
    I am not sure what this means. Please write the question correctly.
    What i wrote there is a complete question....
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  7. #7
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    Re: Series and sequences

    Quote Originally Posted by AuXian View Post
    What i wrote there is a complete question....
    And yet you had to add the phrase "only the final step will convert r to n," the meaning of which I don't understand. Even worse, the left-hand side of the equation in the quote in post #2 does not depend on n (n is a bound variable used as the summation index) while the right hand side does. And if n and r are reversed, then, as post #3 shows, the equation is incorrect.
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