Proving a theory

[squarebear]

I had some spare time yesterday and was thinking about maths and I realised that any odd number can be made from two consecutive numbers. eg:

3+4=7
7+8=15
50+51=101

and so on. I'm sure this has already been discovered before but my question is, how would you prove my "Squarebear theorem" for any odd number, as it was a long time since I did maths at school.

[squarebear]

As they gave 11+3+3 as an example, it is plain to see that any number can be made up of 2 and 3.

7=2+2+3
9=2+2+2+3

and so on...