\(A=1^2+3^2+5^2+...+99^2\)
\(A=1+2^2+3^2+4^2+5^2+...+99^2\)
\(A=1+2.\left(3-1\right)+3.\left(4-1\right)+...+99\left(100-1\right)\)
\(A=\left(2.3+3.4+4.5+...+99.100\right)-\left(1+2+3+...+99\right)\)
\(A=\dfrac{99.100.101}{3}-\dfrac{99.\left(99+1\right)}{2}\)
\(A=333300-4950=32850\)