128k views
4 votes
Find the sum of all positive integers less than 100, which:

are not divisible by 3.

Please tell answer and formula

1 Answer

5 votes

Answer:

The sum of all positive integers less than 100, which are not divisible by 3 is 3267.

Explanation:

The all positive integers less than 100 has sum, given by

S₁ = 1 + 2 + 3 + 4 + ......... + 99

⇒ S₁ =
(99 * (99 + 1))/(2) = 4950

Now, the sum of all positive integers less than 100 which are divisible by 3 is

S₂ = 3 + 6 + 9 + 12 + 15 + ........ + 99

⇒ S₂ = 3(1 + 2 + 3 + ........ + 33)

⇒ S₂ =
3 * (33 * (33 + 1))/(2) = 1683

Therefore, the sum of all positive integers less than 100, which are not divisible by 3 is = S₁ - S₂ = 4950 - 1683 = 3267. (Answer)

Note : The sum of n natural numbers S is given by

S = 1 + 2 + 3 + 4 + ....... + n =
(n * (n + 1))/(2) .

User Jagveer Singh
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories