Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

Answer

3050

Explanation

Integers divisible by 2 are {2,4,6,8,10,..,100}
Integers divisible by 5 are {5, 10, 15,.., 100}
Thus, sum of integers divisible by 2
`= (50)/(2) (2 + 100) = 50 xx 51 = 2550`
Sum of integers divisible by 5
`= (20)/(2) (5 + 100) = 10 xx 105 = 1050`
Sum of integers divisible by 10
`= (10)/(2) (10 + 100) = 5 xx 110 = 550`
`:.` Sum of integers from 1 to 100 divisible by 2 or 5
`= 2550 + 1050 - 550`
`= 2550 + 500 = 3050`