Sum of all natural numbers betwene 500 and 1000 divisnble 13
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the first is 507 = 13·39 and the last is 988 = 13·76
the sum is
S = 13·39 + 13·40 + ... + 13·75 + 13·76 =
= 13(39 + 40 + ... + 75 + 76)
the sum of integers between m and n, m < n is
m + (m + 1) + . . . + (n - 1) + n = (m + n)(n - m + 1)/2
39 + 40 + ... + 75 + 76 = (39 + 76)·(76 - 39 + 1)/2 = 2185
thus
S = 13·2185 = 28405
the first is 507 = 13·39 and the last is 988 = 13·76
the sum is
S = 13·39 + 13·40 + ... + 13·75 + 13·76 =
= 13(39 + 40 + ... + 75 + 76)
the sum of integers between m and n, m < n is
m + (m + 1) + . . . + (n - 1) + n = (m + n)(n - m + 1)/2
39 + 40 + ... + 75 + 76 = (39 + 76)·(76 - 39 + 1)/2 = 2185
thus
S = 13·2185 = 28405
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