Expert: Lynn Houston - 9/8/2009

Question
Hi, I'm in seventh grade, and I'm stuck on this one question . Here it is: Find and record all of the numbers from 1-25 that can be written as the sum of positive integers. I got 1+2=3, but otherwise, I'm stuck. Please Help!
Thanks,
Jessica :)

Answer
1+2=3
2+3=5
3+4=7
4+5=9 etc

Do you see a pattern evolving?  Odd numbers from 3-25 can be written as the sum of 2 consecutive numbers.  The question is, can you use more than 2?

1+2+3=6
2+3+4=9
3+4+5=12
4+5+6=15, etc, so now you also have 6, 12, 18 and 24.  How about 4 consecutive numbers?

1+2+3+4=10
2+3+4+5=14
3+4+5+6=18
4+5+6+7=22, etc, add in 10, 14 and 22

1+2+3+4+5=15
2+3+4+5+6=20
3+4+5+6+7=25  add in 20,

So, 3,5,6,7,9,10,11,12,13,14,15,17,18,19,21,22,23,24,25 can all be written as the sum of consecutive integers.