Answer: 3,267
Explanation:
The first thing is to find the sum of all positive integers less than 100 and also find the sum of all positive integers that are divisible by three , the difference between the two will give the sum of all positive integers less than 100, which are not divisible by 3.
Sum of all positive integers less than 100 implies
1 + 2 + 3 + 4 + ... + 99 , this means there are 99 numbers altogether .
Using the formula for calculating the sum of terms in Arithmetic series , we have :
Sum = n/2 ( a + l)
where n is the number of terms
a is the first term , and
l is the last term
substituting , we have
Sum = 99/ 2 ( 1 + 99)
Sum = 99/2 (100)
Therefore : the sum of all positive integers less than 100 is 4950
Also , sum of all positive integers divisible by 3 implies :
3 + 6 + 9 +... + 99
There are 33 numbers in all
Also using the formula for calculating the sum of terms in Arithmetic series , we have
Sum = n/2 ( a + l )
Sum = 33/2 ( 3 + 99)
sum = 33/2 ( 102)
Sum = 1683
Therefore :the sum of all positive integers less than 100, which are not divisible by 3 implies
4950 - 1683 = 3,267