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.