Find a fast way to sum the integers from 1 to 100?

Gauss' method, supposedly at the age of 5 according to the story ...

Consider pairs:

1 + 100 = 101

2 + 99 = 101

3 + 98 = 101

4 + 97 = 101

5 + 96 = 101

Each pair sums to 101, and there are (100/2) = 50 of them.

So their grand sum is (101 x 50) = 5050.