Sum 1 to N (Gauss)

Sum 1 through N in one step: N × (N+1) ÷ 2.

1 + 2 + 3 + ... + 100 = 5050

Gauss, aged nine, folded the list end to end: 1 + 100, 2 + 99, all 101.

A hundred numbers fold into fifty pairs, so the total is 50 × 101 = 5050.

Any run folds the same way: N / 2 pairs of N + 1, so the sum is N(N + 1) / 2.

Your turn

Three to try in your head — tap what you get.

1 + 2 + ... + 75

1 + 2 + ... + 30

1 + 2 + ... + 10