Question

Tính nhanh:

(20²+18²+16²+...+4²+2²) - (19²+17²+...+3²+1²)

Answer 1

\(\left(20^2+18^2+...+2^2\right)-\left(19^2+17^2+...+1^2\right)\)

\(=20^2+18^2+...+2^2-19^2-17^2-1^2\)

\(=\left(20^2-19^2\right)+\left(18^2-17^2\right)+...+\left(2^2-1^2\right)\)

\(=39+35+31+...+7+3\)

Số số hạng là: \(\left(39-3\right):4+1=10\)

Tổng là: \(\left(39+3\right)\cdot10:2=210\)

Answer 2

\(\left(20^2+18^2+16^2+...+4^2+2^2\right)-\left(19^2+17^2+...+3^2+1^2\right)\)

\(=\left(20-19\right)\left(20+19\right)+\left(18+17\right)\left(18-17\right)+...+\left(4+3\right)\left(4-3\right)+\left(2+1\right)\left(2-1\right)\)

\(=39+35+...+7+3\)

\(=210\)