What do the first ten positive whole numbers add up to?

Adding 1 through 10 gives 55, and the elegant way to see it is to fold the list in half. Pair the first with the last, 1 and 10, then 2 and 9, then 3 and 8, 4 and 7, and 5 and 6. Every pair totals 11, and there are five pairs, so the answer is 5 times 11, or 55. That pairing generalises into a formula that works for any run of consecutive numbers starting at one: multiply the last number by the next one up and halve it. For 100, that gives 100 times 101 divided by 2, which is 5050. The story goes that a young Carl Friedrich Gauss astonished his schoolteacher by producing that result almost instantly, and whether or not the tale is exact, the method is genuine and is the standard way to sum an arithmetic series. Numbers built this way are called triangular numbers, because that many dots form a triangle.

55 is both a triangular number and a Fibonacci number, which is an unusual thing to be.