When expressed as a common fraction, what is the value of (2 + 4 + 6 + 8 + ... + 1340 + 1342)/(3 + 6 + 9 + 12 + ... + 2010 + 2013)?
We can write
2 ( 1 + 2 + 3 + 4 +......+ 670 + 671) 2
____________________________ = ____
3 ( 1 + 2 + 3 + 4 +.......+670 + 671) 3
+16 
