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Successive addition

  1. Mar 29, 2015 #1
    1. The problem statement, all variables and given/known data
    I want to have a formula of this kind,
    (8+7+...+1) + (7+6+..+1) + (6+5+..+1) + ....1

    2. Relevant equations

    3. The attempt at a solution
    I know , n+(n-1)+...+1 = n(n+1)/2
  2. jcsd
  3. Mar 29, 2015 #2


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    So you want a formula for [itex] \frac{n(n+1)}{2}+\frac{(n-1)n}{2}+...[/itex], or [itex] \sum_{k=1}^{n}\frac{k(k+1)}{2}=\frac{1}{2}\sum_{k=1}^{n}(k(k+1))=\frac{1}{2}(\sum_{k=1}^{n}k^{2}+\sum_{k=1}^{n}k)[/itex].
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