Determine the sum for the arithmetic series?

2 Answers

Relevance
  • 8 years ago
    Favorite Answer

    165

  • Brian
    Lv 7
    8 years ago

    sum(m=10 to 20)(30 - m) =

    sum(m=10 to 20)(30) - sum(m=10 to 20)(m) =

    30*sum(m=10 to 20)(1) - [sum(m=1 to 20)(m) - sum(m=1 to 9)(m)] =

    30*(20 - 10 + 1) - [(20*(20 + 1)/2) - (9*(9 + 1)/2)] =

    30*11 - [210 - 45] = 330 - 165 = 165.

    Edit: Note that in general sum(m=1 to n)(m) = n*(n + 1)/2, and that

    sum(m=n to p)(1) = p - n + 1.

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