Solution:

Here's an elegant way:

1 + 32 = 33
2 + 31 = 33
3 + 30 = 33
.....................
.....................
16 + 17 = 33

Adding the above equations gives

1 + 2 + 3 + ....... + 32 = 16 × 33 = 528

Food for thought:

The general formula is:

1 + 2 + 3 + ....... + n = n (n + 1) / 2.

Is the formula valid when n is an odd integer?