\(A=1^2+2^2+3^2+...+200^2\)
\(A=1.1+2.2+3.3+...+200.200\)
\(A=\left(0+1\right).1+\left(1+1\right).2+\left(2+1\right).3+...+\left(199+1\right).200\)
\(A=0.1+1.1+1.2+1.2+2.3+1.3+...+199.200+1.200\)
\(A=\left(1.2+2.3+...+199.200\right)+\left(1.1+1.2+1.3+...+1.200\right)\)
Đặt\(B=1.2+2.3+...+199.200\)
\(3B=1.2.3+2.3.3+...+199.200.3\)
\(3B=1.2.3+2.3\left(4-1\right)+...+199.200\left(201-198\right)\)
\(3B=1.2.3+2.3.4-1.2.3+...+199.200.201-198.199.200\)
\(3B=199.200.201\)
\(B=\dfrac{199.200.201}{3}\)
\(B=2666600\)
\(A=2666600+\left(1.1+1.2+1.3+...+1.200\right)\)
\(A=2666600+\left(1+2+3+...+200\right)\)
\(A=2666600+\dfrac{\left(1+200\right).200}{2}\)
\(A=2666600+20100\)
\(A=2686700\)
