Ta có:
\(10^2+8^2+...+2^2+\left(9^2+7^2+...+1^2\right)\)
\(=1^2+2^2+3^2+4^2+...+8^2+9^2+10^2\)
\(=1.1+2.2+3.3+...+9.9+10.10\)
\(=1\left(2-1\right)+2\left(3-1\right)+3\left(4-1\right)+...+9\left(10-1\right)+10\left(11-1\right)\)
\(=1.2-1+2.3-2+3.4-3+...+10.11-10\)
\(=1.2+2.3+3.4+...+10.11-\left(1+2+3+...+10\right)\)
Đặt \(A=1.2+2.3+3.4+...+10.11\)
\(3A=1.2.3+2.3.3+3.4.3+...+10.11.3\)
\(3A=1.2\left(3-0\right)+2.3\left(4-1\right)+3.4\left(5-2\right)+...+10.11\left(12-9\right)\)
\(3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+10.11.12-9.10.11\)
\(3A=10.11.12\)
\(3A=1320\)
\(A=440\)
Đặt B = 1 + 2 + - + 10
=> B = 55
=> A - B = 440 - 55 = 385
Vậy biểu thức trên bằng 385
