How many candles do we light on Chanukah? There are two ways to calculate this. One is to add up every number from 2 (1 + a shamash) through 9 (8 + a shamash) = 44. The other is to recognize that this is an arithmetic series and use the simple formula: 1/2 * n * (A1 + An) = 1/2 * 8 * (2 + 9) = 44.
Now calculate how many candles you would have to light if Chanukah was 15 days or 30 days (135 and 495).
Legend has it that the basis of this formula was figured out by an elementary school student named Carl Friedrich Gauss, when his teacher told the class to add up all the numbers from 1 to 100 and he was able to do it in a few seconds (more info: I, II).
R. Mordechai Marcus once told me that there is a Tosafos, I don’t remember where but perhaps in
Bekhoros [Menachos 106a s.v. she-hein elef], that offers a similar formula.
(inspired by an e-mail from Dr. Yitzchak Levine)