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# What is the sum of all integers not greater than 10000 that are not divisible by 7?

Updated: 9/18/2023

Wiki User

13y ago

Best Answer

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

Wiki User

13y ago
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