Starting at the age of 1, I get a dollar. Age 2 I get $2. Age 3 I get $3…If I save every dollar I get, how much money would I have when I reach 100 years old?
It's called an arithmetic sequence ('s sum). The anecdote goes that gauss received this problem from an ill tempered teacher, but noticed that by pairing up the highest and lowest numbers - excluding 50 - the pair's sum is always 101, and there are half as many pairs as numbers in the sequence, so a simple multiplication gives the solution.