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Math Help - Method of difference?

  1. #1
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    Method of difference?

    One formula is like this : f(r) - f(r + 1) and another is f(r) - f(r -1). Sometimes, I see them change to f(r) - f(r + 2), etc...I'm very confused. Which is which and how do I know which one to use for which question? There was one time I used f(r) - f(r + 1) and it was wrong but when I used f(r) - f(r - 1), it was correct. I've forgotten which question because it was on the net. Thanks.
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  2. #2
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    Quote Originally Posted by mark1950 View Post
    One formula is like this : f(r) - f(r + 1) and another is f(r) - f(r -1). Sometimes, I see them change to f(r) - f(r + 2), etc...I'm very confused. Which is which and how do I know which one to use for which question? There was one time I used f(r) - f(r + 1) and it was wrong but when I used f(r) - f(r - 1), it was correct. I've forgotten which question because it was on the net. Thanks.
    Hi

    It depends on the question .

    Example : If this is the question

    \sum^{n}_{r=1}(\frac{1}{r}-\frac{1}{r+1})

    Let f(r)=\frac{1}{r} , then f(r+1)=\frac{1}{r+1}

    So \sum^{n}_{r=1}[f(r)-f(r+1)]

    Or if you get another question like this

    \sum^{n}_{r=1}[\frac{1}{r+1}-\frac{1}{r}]

    Then you let  f(r)=\frac{1}{r+1} ,  f(r-1)=\frac{1}{r}

    So \sum^{n}_{r=1}[f(r)-f(r-1)]

    Hope that helps .
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