Tính: 1 × 2 + 2 × 3 + 3 × 4 + ... + 38 × 39 + 39 × 40.

S = 1 × 2 + 2 × 3 + 3 × 4 + ... + 38 × 39 + 39 × 40

3S = 1 × 2 × 3 + 2 × 3 × 3 + 3 × 4 × 3 + ... + 38 × 39 × 3 + 39 × 40 × 3

3S = 1 ×2 × 3 + 2 × 3 × (4 ‒ 1) + 3 × 4 × (5 ‒ 2) + ... + 38 × 39×(40 ‒ 37) + 39 × 40 × (41 ‒ 38)

3S = 1 × 2 × 3 + 2 × 3 × 4 ‒ 1 × 2 × 3 + 3 × 4 × 5 ‒ 2 × 3 × 4 + ... + 38 × 39 × 40 ‒ 37 × 38 × 39 + 39 × 40 × 41 ‒ 38 × 39 × 40

3S = 39 × 40 × 41

Suy ra S = (39 × 40 × 41) : 3

Vậy S = 21 320.