In the list below I have tried to express each integer 1-9 as a sum of consecutive positive integers:

1 = ?
2 = ?
3 = 1+2
4 = ?
5 = 2+3
6 = 1+2+3
7 = 3+4
8 = ?
9 = 2+3+4

This suggest that there is a sum for every positive integer which is not a power of 2, and there is never a sum for powers of 2.

Prove or disprove my claims.