The anecdote of the young Gauss

History — The anecdote of the young Gauss

The story goes that Gauss’s teacher, to keep the class busy, asked them to add up the numbers from $1$ to $100$. Young Carl Friedrich, after a few seconds, wrote $5050$. He had noticed: $1+100 = 2+99 = \cdots = 50+51 = 101$, there are $50$ pairs, hence $50\cdot 101 = 5050$. This is exactly the formula $S_n = n(a_1+a_n)/2$ with $a_1 = 1$, $a_n = 100$, $n = 100$.

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Topics: Sequences
Concepts: Arithmetic progression
Methods: Sum of an arithmetic progression
People: Carl Friedrich Gauss