\(G=1\times2+2\times4+3\times5+....+99\times101\)
\(=\left(2-1\right)\left(2+1\right)+\left(3-1\right)\left(3+1\right)+\left(4-1\right)\left(4+1\right)+...+\left(100-1\right)\left(100+1\right)\)
\(=2^2-1+3^2-1+4^2-1+....+100^2-1\)
\(=1^2+2^2+3^2+....+100^2-1\times100\)
Áp dụng công thức :
\(1^2+2^2+3^2+4^2+....+n^2=\dfrac{n\left(n+1\right)\left(2n+1\right)}{6}\)
\(\Rightarrow\dfrac{100\left(100+1\right)\left(200+1\right)}{6}-100\)
\(=338250\)
Vậy \(G=338250\)
~ Học tốt ~
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