Solution:

Here's an elegant way:

1 + 42 = 43
2 + 41 = 43
3 + 40 = 43
.....................
.....................
21 + 22 = 43

Adding the above equations gives

1 + 2 + 3 + ....... + 42 = 21 × 43 = 903

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?