A quick selection from Proof and the Art of Mathematics
I did it in terms of partial sums. For example the sum
1 + 2 + 5 + 2
corresponds to the partial sums 1, 3, 8, 10.
The largest partial sum is always n. The other partial sums can be any subset of {1, 2, ..., n-1}. Hence there are 2^(n-1) possible sums.
That is a great argument. Wonderful!
I did it in terms of partial sums. For example the sum
1 + 2 + 5 + 2
corresponds to the partial sums 1, 3, 8, 10.
The largest partial sum is always n. The other partial sums can be any subset of {1, 2, ..., n-1}. Hence there are 2^(n-1) possible sums.
That is a great argument. Wonderful!