\(S=1^2+2^2+3^2+...+51^2\)
\(S=1\left(2-1\right)+2\left(3-1\right)+3\left(4-1\right)+...+51\left(52-1\right)\)
\(S=1.2-1.1+2.3-1.2+3.4-1.3+...+51.52-1.51\)
\(S=\left(1.2+2.3+3.4+...+51.52\right)-\left(1+2+3+...+51\right)\)
Đặt \(A=1.2+2.3+3.4+...+51.52\)
\(3A=1.2.3+2.3.3+3.4.3+...+51.52.3\)
\(3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+51.52.\left(53-50\right)\)
\(3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+51.52.53-50.51.52\)
\(3A=51.52.53\)
\(A=\frac{51.52.53}{3}=46852\)
\(\Rightarrow\)\(S=A-\left(1+2+3+...+51\right)=46852-1326=45526\)
Vậy \(S=45526\)
Chúc bạn học tốt ~
\(S=1.1+2.2+3.3+.......+51.51\)
\(S=1\left(2-1\right)+2\left(3-1\right)+3\left(4-1\right)+.............+51\left(52-1\right)\)
\(S=1.2+2.3+3.4+.....+51.52-1-2-3-4-5-........-51\)
\(3S=1.2.\left(3-0\right)+.........+51.52.\left(53-50\right)-\left(1+2+3+.......+51\right).3\)
\(3S=51.52.53-52.51:2.3\)
\(...............................................\)
