Question

Find the sum of every even positive integer less than 233 not divisible by 10___ .

Answer 1

We find the sum of all positive even integers less than 233 and then subtract all the positive integers less than 233 that are divisible by 10.
2+4+....+232 = 2(1+2+. . . +116) = 116 .117 = 13572.

The sum of all positive integers less than 233 that are divisible by 10 is 10+20+. . .+230 = 10(1+2+. . .+23) = 2760. Then our answer is 13572-2760 = 10812.