2010 is divisible by 3, so the largest integer less than 2010
that is divisible by 3 is 3 less that 2010, or 2007

First use the sum formula to find the sum of ALL integers less than
2010, which are the integers 1,2,3,...,2009

Sn = (a1 + an) 

with n=2009, a1 = 1,  an = 2009, to find the sum of all
positive integers less than 2010, the integers 1,2,3,...,2009.

Now we need to find the sum of the integers which are divisible by 3.
They are these: 

3,6,9,...,2007

We can find n, which is how many there are, by thinking of dividing 
them all by 3 and getting 

1,2,3,...669

So we know there are 669 multiples of 3 less than 2010.  So we
use the sum formula again

Sn = (a1 + an) 

this time with n=669, a1 = 3,  an = 2007 
to find the sum of all integers divisible by 3 which are less 
than 2010, which are 3,6,9,...,2007.

Then finally, to find the sum of all positive integers which are 
less than 2010 and are not divisible by 3, we subtract the second
number from the first number.

Answer:  672345

Edwin