Giải:
Đặt \(A=50^2-49^2+48^2-47^2+...+2^2-1^2\)
\(\Leftrightarrow A=\left(50^2-49^2\right)+\left(48^2-47^2\right)+...+\left(2^2-1^2\right)\)
\(\Leftrightarrow A=\left(50-49\right)\left(50+49\right)+\left(48-47\right)\left(48+47\right)+...+\left(2-1\right)\left(2+1\right)\)
\(\Leftrightarrow A=50+49+48+47+...+2+1\)
\(\Leftrightarrow A=\dfrac{\left(50+1\right).50}{2}\)
\(\Leftrightarrow A=1275\)
Vậy giá trị của biểu thức \(50^2-49^2+48^2-47^2+...+2^2-1^2\) là 1275.
Chúc bạn học tốt!!!
\(50^2-49^2+48^2-47^2+...........+2^2-1^2\)
\(=\left(50^2-49^2\right)+\left(48^2-47^2\right)+.......+\left(2^2-1^2\right)\)
\(=\left(50-49\right)\left(50+49\right)+\left(48-47\right)\left(48-47\right)+.......+\left(2-1\right)\left(2+1\right)\)
\(=50+49+..........+1\)
\(=\dfrac{\left(50+1\right)50}{2}=1275\)
