Here is a formula for the sum of the first *n* natural numbers:

One example of this is . Gauss as a small
child is said to have calculated this by noticing that 1+100=101,
2+99=101, 3+98=101, etc., so the entire sum is 50(101)=5050.
We can use this idea to prove the formula. Let *S* be the sum. Then

Adding these together yields

So *S*=*n*(*n*+1)/2.

Wed Apr 21 08:17:28 EDT 1999