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What is the sum of all integers not greater than 10000 that are not divisible by 7?
This is easiest to answer by summing all the numbers 1-10000 and subtracting the sum of the multiples of 7 (7, 14, 21, ..., 9996).
The sum of a series is:
S = (first + last) x number_of_terms / 2
For for 1-10000, the sum is:
S1 = (1 + 10000) x 10000 / 2
= 10001 x 5000
= 50005000
For the multiples of 7 the sum is:
S2 = (7 + 9996) x 1428 / 2
= 10003 x 714
= 7142142
So the sum of all integers not greater than 10000 that are not divisible by 7 is:
S = S1 - S2
= 50005000 - 7142142
= 42,862,858
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