Find the sum of integers from 11 to 1000 which are divisible by 3.

Given, Sum of integers from 11 to 1000

we need to find out the numbers which are divisible by 3

⇒ Now, Sum of integers form 1 to N =

⇒ Sum of integers divisible by 3 from 11 to 1000 = Sum of integers divisible by 3 from 1 to 1000 – Sum of integers divisible by 3 from 1 to 10

= (3 + 6 + 9………. + 999) – (3 + 6 + …. + 9)

= 3(1 + 2 + 3…… + 333)-3(1 + 2 + .. + 3)

=

=

= 3(333(167)) – 3(6)

= 3(55611)-18

= 166833-18

= 166815

Hence, the sum of integers from 11 to 1000 which are divisible by 3 is 166815.