The sum of all natural numbers less than or equal to 500 that are divisible by 3 or 5 , but not divisible by 2 , is

Step-by-step solution

We need to find the sum of all odd multiples of 3 and odd multiples of 5 up to 500 , and subtract the sum of their common odd multiples (odd multiples of 15 ) to avoid double counting. Sum of odd multiples of 3 up to 500 : The sequence is 3, 9, 15, , 495 . This can be written as 3(1, 3, 5, , 165) . The number of terms is given by 2n - 1 = 165 n = 83 . The sum of the first n odd natural numbers is n^2 . Sum = 3 (83)^2 = 3 6889 = 20667 . Sum of odd multiples of 5 up to 500 : The sequence is 5, 15, 25, , 495 . This ca