Carl Friedrich Gauss

There is a story about the 7-year-old, German, mathematician Carl Friedrich Gauss. He responded to his teacher, Büttner's, request to sum the first 100 counting numbers (1 to 100). While his classmates toiled, Carl wrote a single number and handed it in. He was correct.

 Gauss on the old Deutsche Mark

When asked how he did it, he explained that there were 50 pairs of numbers adding to 101. So, the sum must be 50 x 101 = 5050.

Here's he formula: (n*(n+1))/2

That version requires an even quantity and the first integer is 1.

For example: start easy and ask yourself:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = ?

Here's Gauss applied:

1. [1 + 10 = 11]
2. [2 + 9 = 11]
3. [3 + 8 = 11]
4. [4 + 7 = 11]
5. [5 + 6 = 11]

So, it's 11 five times; that's 55, right? Check a calculator.

This simple formula has saved me lots of time.