1. ## Consecutive numbers

can anyone shed any light on this problem. i don't know where to start!

'Many numbers can be expressed as the sum of two or more consecutive integars.

For example:
15=7+8
10=1+2+3+4

Can you say which numbers can be expressed this way and which numbers cannot be?

So I understand that I have to go through the numbers and work out which are and aren't (e.g 1+2=3 so 3 works, then the next that works would be 2+3=5).

Can anyone see any particular ways I should go about doing this? Also what does it mean by can you prove your statements?

Any suggestions?

2. What level of math are you in? (I don't want to give too confusing an answer)

3. Originally Posted by xjx
can anyone shed any light on this problem. i don't know where to start!

'Many numbers can be expressed as the sum of two or more consecutive integars.

For example:
15=7+8
10=1+2+3+4

Can you say which numbers can be expressed this way and which numbers cannot be?

So I understand that I have to go through the numbers and work out which are and aren't (e.g 1+2=3 so 3 works, then the next that works would be 2+3=5).

Can anyone see any particular ways I should go about doing this? Also what does it mean by can you prove your statements?

Any suggestions?
The sum of n terms of an arithmetic progressiosn with first term a1
and common difference d is:

Sn=a1 + a2 + ... + an=n.a1+n(n-1)d/2.

So the sum of consecutive integers will be such a sum with a common
difference d=1, so

Sn=n.a1+n(n-1)/2,

which is the (n-1)th triangular number plus some multiple of n.

RonL

4. I answered this question a long time ago, those numbers that are exponents of two cannot be expressed as a sum of consecutives.