SOLUTION: Find the sum of all positive integers less than 100 that are divisible by three but not two. Show or explain how you got your answer.

Question 558680: Find the sum of all positive integers less than 100 that are divisible by three but not two. Show or explain how you got your answer.

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Sum = 3+9+15+...+93+99

Use the "Gauss" method where you list the addends in reverse order:

Sum = 3+9+15+...+93+99
Sum = 99+93+...+9+3

2*Sum = 102+102+... = 102*17 (102 occurs 17 times)

Sum = 51*17 = 867

Update: There isn't really much of an "algebraic" solution since we know the numbers we wish to add are the odd multiples of 3 (3, 9, 15, ..., 99) and adding them doesn't require much algebra. Even with an "algebraic" solution you should still obtain the same answer.
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