Ta có: \(50^2-49^2+48^2-47^2+....+2^2-1^2\)
\(=\left(50^2-1^2\right)-\left(49^2-2^2\right)-\left(48^2-3^2\right)-...-\left(27^2-24^2\right)-\left(26^2-25^2\right)\)
\(=\left(51\cdot49\right)-\left(51\cdot47\right)-\left(51\cdot45\right)-....-\left(51\cdot3\right)-\left(51\cdot1\right)\)
=51(49-47-45-...-3-1)
=51*25
=1275