Young Gauss paired the numbers — 1+100, 2+99, 3+98 — into 50 pairs that each total 101, giving 5,050.
Carl Friedrich Gauss reportedly did this in class while his teacher expected an hour of quiet. Fifty pairs, each summing to 101, make 50 × 101 = 5,050. It is the pairing trick in action — the same idea behind the series formula.
