How Many Ways Can a Number Be Represented as an Arithmetic Series Sum?

[Natasha1]

I have been asked to write up a 20 page report on the following...

For example 2 + 3 + 4 = 9 or 7 + 8 + 9 +10 = 34

Investigate this theme? (Hints from my teacher how many ways can a number be thus obtained? Could you specify which numbers can be done in just one way, two ways, etc. Use the arithmetic series sum formula)

What's this all about? heeeeeeeeeeeeeeeeeeeelp please

Any further thoughts welcome ;)

 

[courtrigrad]

heres a good place to start http://mathworld.wolfram.com/ArithmeticSeries.html