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Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Weekly Problem 14 - 2011

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

The sum of three numbers is $2009$. The sum of the first two numbers is $1004$ and the sum of the last two is $1005$. What is the product of all three numbers?
 
 
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
 
 

This problem is taken from the UKMT Mathematical Challenges.

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