Question

\((50^2+48^2+...+2^2)-(49^2+47^2+...+1^2)\)

Answer 1

\(\left(50^2+48^2+...+2^2\right)-\left(49^2+47^2+...+1^2\right)\)

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

\(=\left(50^2-49^2\right)+\left(48^2-47^2\right)+...+\left(2^2-1^2\right)\)

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

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

\(=\dfrac{50\left(50+1\right)}{2}=\dfrac{50\cdot51}{2}=1275\)

Answer 2

Ta có : ( 50² + 48² + ... + 2² ) - ( 49² +47² + ... + 1² )

= 50² + 48² +...+ 2² - 49² -47² - 1²

\(=\left(50^2-49^2\right)+\left(48^2-47^2\right)+...+\left(2^2-1^2\right)\)

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

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

= \(1257\)