Gauss' punishment

Remarks.

Johann Carl Friedrich Gauss (30 Apr 1777 – 23 Feb 1855) was a German mathematician,
astronomer, geodesist and physicist who contributed to many fields in mathematics and science. He is
widely considered one of the greatest mathematicians of all time. In H2 Mathematics, you will encounter many mathematical concepts which are formalized or introduced by him, e.g., normal distribution, complex numbers, etc. Quoting from “Gauss’s Day of Reckoning” 1published in The American Scientist:

“In the 1780s a provincial German schoolmaster gave his class the tedious assignment of summing the first 100 integers. The teacher’s aim was to keep the kids quiet for half an hour, but one young pupil almost immediately produced an answer: \(1 + 2 + 3 + … + 99 + 100 = 5050\). The smart aleck was Carl Fredrich Gauss, who would go on to join the short list of candidates for greatest mathematician ever. Gauss was not a calculating prodigy who added up all those numbers in his head. He had a deeper insight: If you “fold” the series of the numbers in the middle and add them in pairs – \(1 + 100, 2 + 99, 3 + 98, …, \) and so on – all the pair sum to \(101\). There are \(50\) such pairs, and so the grand total is simply \(50 × 101\). The more general formula, for a list of consecutive integers from 1 through \(n\) is \(n(n + 1)/2\).”

The closed formula for an arithmetic series can thus be credit to Gauss.