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    Right, so I was working through a past paper (OCR, non MEI, Jan 08) and I got stuck on question 10. The bit that's causing me the problem is part 2 of the question, where you are asked to find an expression in terms of n for: \displaystyle\sum_{r=1}^{n} \displaystyle\frac{3r+4}{r(r+1)(  r+1)}.

    The only thing that sprung to my mind was to use the method of differences with: \displaystyle\sum_{r=1}^{n} \displaystyle\frac{2}{r} - \displaystyle\sum_{r=1}^{n} \displaystyle\frac{1}{(r+1)(r+2)  }. But I couldn't find a pattern.


    Am I even on the right tracks because I have no idea what I'm doing?


    Zacken, I know you like these
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    (Original post by Andy98)
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    Partial fractions gets you: \displaystyle \frac{3r+1}{r(r+1)(r+2)} = \frac{2}{r} - \frac{1}{r+1} - \frac{1}{(r+2)}.
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    (Original post by Andy98)
    Right, so I was working through a past paper (OCR, non MEI, Jan 08) and I got stuck on question 10. The bit that's causing me the problem is part 2 of the question, where you are asked to find an expression in terms of n for: \displaystyle\sum_{r=1}^{n} \displaystyle\frac{3r+1}{r(r+1)(  r+1)}.

    The only thing that sprung to my mind was to use the method of differences with: \displaystyle\sum_{r=1}^{n} \displaystyle\frac{2}{r} - \displaystyle\sum_{r=1}^{n} \displaystyle\frac{1}{(r+1)(r+2)  }. But I couldn't find a pattern.


    Am I even on the right tracks because I have no idea what I'm doing?




    Zacken, I know you like these

    you split in 3 fractions
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    (Original post by Andy98)
    Right, so I was working through a past paper (OCR, non MEI, Jan 08) and I got stuck on question 10. The bit that's causing me the problem is part 2 of the question, where you are asked to find an expression in terms of n for: \displaystyle\sum_{r=1}^{n} \displaystyle\frac{3r+1}{r(r+1)(  r+1)}.

    The only thing that sprung to my mind was to use the method of differences with: \displaystyle\sum_{r=1}^{n} \displaystyle\frac{2}{r} - \displaystyle\sum_{r=1}^{n} \displaystyle\frac{1}{(r+1)(r+2)  }. But I couldn't find a pattern.


    Am I even on the right tracks because I have no idea what I'm doing?


    Zacken, I know you like these
    I would suggest partial Fractions and then the methord of differences.
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    (Original post by Zacken)
    Partial fractions gets you: \displaystyle \frac{3r+1}{r(r+1)(r+2)} = \frac{1}{2r} + \frac{2}{r+1} - \frac{5}{2(r+2)}.
    (Original post by TeeEm)
    you split in 3 fractions
    *******s, made a typo; see the edit
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    (Original post by Andy98)
    *******s, made a typo; see the edit
    See mine. Your edit it makes it work out much better.
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    (Original post by Zacken)
    Partial fractions gets you: \displaystyle \frac{3r+1}{r(r+1)(r+2)} = \frac{2}{r} - \frac{1}{r+1} - \frac{1}{(r+2)}.
    (Original post by Zacken)
    See mine. Your edit it makes it work out much better.
    Thanks, so my idea of trying to keep it to two fractions was the problem?
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    (Original post by Andy98)
    Thanks, so my idea of trying to keep it to two fractions was the problem?
    Yup. You should always decompose the fractions. Remember, you want your summation to be of the form f(r) - f(r+k) so that they cancel. This works out if you decompose it into three different fractions.
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    (Original post by Zacken)
    Yup. You should always decompose the fractions. Remember, you want your summation to be of the form f(r) - f(r+k) so that they cancel. This works out if you decompose it into three different fractions.
    Ahhh, that makes more sense, thanks dude. The way my teacher taught it made it sound like we just broke it into two bits
 
 
 
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