Tổng quát: \(\frac{2}{\left(a-1\right).a.\left(a+1\right)}=\frac{1}{a\left(a-1\right)}-\frac{1}{a\left(a+1\right)}\)

Ta có:\(2A=2.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+....+\frac{1}{37.38.39}\right).1428+185.8\)

\(\Leftrightarrow2A=\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+....+\frac{2}{37.38.39}\right).1428+185.8\)

\(\Leftrightarrow2A=\left[\left(\frac{1}{1.2}-\frac{1}{2.3}\right)+\left(\frac{1}{2.3}-\frac{1}{3.4}\right)+...+\left(\frac{1}{37.38}-\frac{1}{38.39}\right)\right].1428+185.8\)

\(\Leftrightarrow2A=\left(\frac{1}{1.2}-\frac{1}{38.39}\right).1428+185.8=\frac{541680}{247}\)

\(\Leftrightarrow A=\frac{541680}{494}=1096,518219\approx1096,5\)

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