=(502-492)+...+(22-12)
=(50-49)(50+49)+(48-47)(48+47)+...+(2-1)(2+1)
=1.99+1.95+1.91+...+1.3
=99+95+91+...+3
=(99+3)+(95+7)+...+
\(50^2-49^2+48^2-47^2+...+2^2-1^2\)
\(=\left(50^2-49^2\right)+\left(48^2-47^2\right)+...+\left(2^2-1^2\right)\)
\(=\left(50+49\right)\left(50-49\right)+\left(48+47\right)\left(48-47\right)+...+\left(2+1\right)\left(2-1\right)\)
\(=99.1+95.1+...+3.1\)
\(=99+95+...+3\)
\(=3+...+95+99\)
Từ 3 đến 99 có: \(\left(99-3\right):4+1=25\left(\text{số hạng}\right)\)
Tổng là: \(\frac{\left(99+3\right)\times25}{2}=1275\)
\(=\left(50^2-49^2\right)+\left(48^2-47^2\right)+...+\left(2^2-1^2\right)\)
\(=\left(50-49\right).\left(49+50\right)+\left(48-47\right).\left(47+48\right)+....+\left(2-1\right).\left(1+2\right)\)
\(=50+49+48+...+2+1\)
\(=\frac{\left[\left(50-1\right):1+1\right].\left(50+1\right)}{2}=25.51=1275\)
