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, omitting the multiples of 3.

Algebra ->  Sequences-and-series -> 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, omitting the multiples of 3.      Log On


   

Question 1034630: 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, omitting the multiples of 3.
Answer by ikleyn(52788) About Me  (Show Source):
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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,
omitting the multiples of 3.
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Calculate the sum of all integers from 1 to 300 inclusively.

It is %28300%2A301%29%2F2 = . . .     (1)   (calc it yourself)  

(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). 

Again, use the formula for the sum of AP.

It is 3%2A%28%28100%2A101%29%2F2%29.          (2)

As a final step, distract (2) from (1).