The sum of all number between 500and 1000 which are divisible by 13
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find the sum of multiples of 13 between 500 & 1000
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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503+520+533+546+559+572+585+598+611+624+637+650+663+676+689+702+715+728+741+754+767+780+793+806+819+832+845+858+871+884+897+910+923+936+949+962+975+988
=28405
hope this helps and mark me as brainliest if it does please please...
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