Question

[Lê khắc Tuấn Minh]

Tính nhanh

\(\left(50^2+48^2+46^2+....+4^2+2^2\right)-\left(49^2+47^2+45^2+...+5^2+3^2+1^2\right)\)

Answer 1

[Nguyễn Đình Dũng]

(50²+48²+...+2²) - (49²+47²+...+1²)

= (50²-49²) + (48²-47²) + ... + (2²-1²)

= (50+49)(50-49) + (48+47)(48-47) + ... + (2+1)(2-1)

= 50+49+48+47+...+1

= \(\frac{\left(50+1\right).50}{2}=\frac{51.50}{2}=1275\)