Question

Find the sum of all integers between 100 and 200 which are not divisible by 9

Answer 1

The integers between 100 and 200 divisible by 9 are 108, 117, 126, ....., 198.
Number of integers is
$\frac{198 - 108}{9} + 1 = 11$
Sum of these integers is
$\frac{11}{2} \times (108 + 198) = 1683$
All integers between 100 and 200 are
101, 102, ...., 199
Number of integers is (199 - 101) + 1 = 99
Sum of these integers is
$\frac{99}{2} \times (101 + 199) = 14850$

Therefore, sum of integers not divisible by 9 is 14850 - 1683 = 13167