\(D=\left(50^2+48^2+46^2+..+2^2\right)-\left(49^2+47^2+..+1^2\right)\)
\(=50^2+48^2+46^2+..+2^2-49^2-47^2-...-1^2\)
\(=\left(50^2-49^2\right)+\left(48^2-47^2\right)+...+\left(2^2-1^2\right)\)
\(=\left(50-49\right)\left(50+49\right)+\left(48-47\right)\left(48+47\right)+...+\left(2-1\right)\left(2+1\right)\)
\(=50+49+48+47+...+1\)
=\(\frac{\left(50+1\right)\cdot50}{2}=1275\)
Đặt A = 50^2 - 49^2 + 48^2 - 47^2 + ... + 2^2 - 1^2.
<=> A = (50 - 49)(50 + 49) + (48 - 47)(48 + 47) + ... + (2 - 1)(2 + 1)
= 99 + 95 + .. + 3
= (99 + 3)[(99 - 3) : 4 + 1] : 2 (cách tính tổng của dãy số cách đều)
= 1275.
(50^2+48^2+46^2+...+4^2+2^2)-(49^2+47^2+45^2+...+5^2+3^2+1^2)
=(50^2-49^2)+(48^2-47^2)+...+(2^2-1^2)
=(50+49)(50-49)+(48+47)(48-47)+...+(2+1)(2-1)=50+49+48+47+...+2+1
=\(\frac{50.51}{2}\)
=1275
