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Math Help - sum of the integers

  1. #1
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    sum of the integers

    Prove that the sum of all positive integers between m and n inclusive (n>m) is 1/2(m+n)(n-m+1).
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  2. #2
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    Sum of AP

    Hello thereddevils
    Quote Originally Posted by thereddevils View Post
    Prove that the sum of all positive integers between m and n inclusive (n>m) is 1/2(m+n)(n-m+1).
    Do you know how to find the sum of an arithmetic progression (AP)? One formula (there are other versions of it) you can use is

    S = \frac{n}{2}(a+l)

    where a and l are the first and last terms, and n is the number of terms.

    Now we want the sum of all the integers between m and n inclusive. So that is

    m + (m+1) + ... + n

    And this is an AP where a = m, l = n and the number of terms is n - (m-1) = n - m + 1

    So plug these values into the formula above, and the sum is

    \tfrac{1}{2}(m+n)(n-m+1)

    Grandad
    Last edited by Grandad; February 23rd 2009 at 02:51 AM. Reason: Simplified solution
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