Maths 公式與代入法

28.
已知 1² + 2² + ... + n² = n(n + 1)(2n + 1)/6

代 n = 20 可得
1² + 2² + ... + 20²
= 20(20 + 1)(2 × 20 + 1)/6
= 20(21)(41)/6
= 10(7)(41)
= 70(41)
= 2870

1^2 + 2^2 + ... + 20^2
=20(20+1)(2*20+1)/6
=2870