SOLUTION: What is the sum of all the multiples of 4 through 4000?

Question 723119: What is the sum of all the multiples of 4 through 4000?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
That is the sum of an arithmetic sequence with 1000 terms.
It is easy to see that the sum,
4+8+12+ .... +3992+3996+4000 is half of
(4+8+12+ .... +3992+3996+4000) + (4000+3996+3992+ .... +12+8+4) = (4+4000)+(8+3996)+(12+3992)+ ... +(3992+12)+(3996+8)+(4000+4)=4004+4004+4004+ ... +4004+4004+4004=1000*4004=4004000
So the sum is .

We could write some fancy formulas, like
, , ,
and in this case
In this case,

and in this case

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