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

Given, Sum of integers from 1 to 100

Need to find out the numbers which are divisible by 2 or 5.

⇒The numbers which are divisible by 2 are 2,4,6….100

And the numbers which are divisible by 5 are 5,10,15…..100

⇒ Sum numbers are repeated twice hence, we need to take the LCM of 2 and 5 which is 10

∴ sum of numbers which are divisible by 10 are 10,20……100

⇒ Now, Sum of integers form 1 to N =

∴ Sum of integers divisible by 2 or 5 from 1 to 100 = Sum of integers from 1 to 100 divisible by 2 + Sum of integers from 1 to 100 divisible by 5 – Sum of integers from 1 to 100 divisible by 10

= (2 + 4….. + 100) + (5 + 10 + ….. + 100)-(10 + 20 + …… + 100)

= 2(1 + 2 + … + 50) + 5(1 + 2 + …. + 20)-10(1 + 2 + ….. + 10)

= (50 × 51) + (5 × 10 × 21)-(5 × 10 × 11)

= 2550 + 1050-550

= 3050

Hence, the sum of integers from 1 to 100 which are divisible by 2 or 5 is 3050