SOLUTION: Find the sum of the series 1 + 2 + 4 + 5 + 7 + 8 + 10 + 11 + ... + 299, which is the sum of the integers from 0 to 300, leaving out the multiples of 3.

Question 1035578: Find the sum of the series 1 + 2 + 4 + 5 + 7 + 8 + 10 + 11 + ... + 299, which is the sum of the integers from 0 to 300, leaving out the multiples of 3.
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
.

Calculate the sum of all integers from 1 to 300 inclusively.

It is  = 45150.     (1) 

(use the known formula for the sum of arithmetic progression.
See the lesson Arithmetic progressions in this site).

Next, calculate the sum of the integers from 0 to 300 that are multiples of 3.

It is 3*(1 + 2 + 3 + . . . + 100) =  = 3*5050 = 15150.   (2)

Again, use the formula for the sum of AP.

As a final step, distract (2) from (1): 45150 - 15150 = 30000.

Answer.  30000.

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