Consider the multiples of four from 0 to 1000. Calculate the sum of these multiples. Show your work for how you determined the answer. Write the sum in summation notation.

Answer 1

sum of all integers from 0 to 1000 is given by Gauss' formula

n(n+1)/2 = 1000(1001)/2 = 500(1001) =500500

but you want only the sum of 4,8, 12, 16, ....996, 1000.

that's the same as 4 times 1,2,3, ...249, 250

use Gauss' formula for sum of 1 through 250 = 250(251)/2 = 125(251) =31,375 multiply that times 4 to get

125,500

If you want summation notation, use a Greek capital sigma. put i=1 at the bottom below the Sigma and 250 on the top. 4 Sigma i = 125,500