Question

What is the sum of all positive integers less than 300 which are divisible by 3

Answer 1

14,850

Explanation:

You need the sum of

3 + 6 + 9 + 12 + ... + 294 + 297

Factor out a 3 from the sum

3 + 6 + 9 + 12 + ... + 294 + 297 = 3(1 + 2 + 3 + 4 + ... + 98 + 99)

You need to add all integers from 1 to 99 and multiply by 3.

The sum of all consecutive integers from 1 to n is:

[n(n + 1)]/2

The sum of all consecutive integers from 1 to 99 is

[99(99 + 1)]/2

The sum you need is 3 * [99(99 + 1)]/2

3 + 6 + 9 + 12 + ... + 294 + 297 =

= 3 * [99(99 + 1)]/2

= 3 * [99(100)]/2

= 3 * 9900/2

= 14,850