\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{37.38.39}\)
\(A=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{37.38}-\frac{1}{38.39}\right)\)
\(A=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{38.39}\right)\)
\(A=\frac{1}{2}.\frac{370}{741}\)
\(A=\frac{185}{741}\)
\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{37.38.39}\)
\(\Leftrightarrow\frac{1}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{37.38.39}\right)\)
\(\Leftrightarrow\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{37.38}-\frac{1}{38.39}\right)\)
\(\Leftrightarrow\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{38.39}\right)\)
Tự tính tiếp nha =)) mỏi tay quá
\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+......+\frac{1}{37.38.39}\)
\(=\) \(1-\frac{1}{2}-\frac{1}{3}+\frac{1}{2}-\frac{1}{3}-\frac{1}{4}+\frac{1}{3}-\frac{1}{4}-\frac{1}{5}+.......+\frac{1}{37}-\frac{1}{38}-\frac{1}{39}\)
\(=\)\(1-\frac{1}{39}\)
\(=\)\(\frac{38}{39}\)
Vậy \(A=\frac{38}{39}\)
2A=2/1.2.3+1/2.3.4+...+2/37.38.39
2A=1/1.2 - 1/2.3+1/2.3 - 1/3.4+...+1/37.38 - 1/38.39
2A=1/2 - 1/1482
2A=370/741
A=370/741:2
A=370/741.1/2=185/741
\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{37.38.39}\)
\(A:4=\frac{1}{1.2.3.4}+\frac{1}{2.3.4.\left(5-1\right)}+\frac{1}{3.4.5.\left(6-2\right)}+...+\frac{1}{37.38.39.\left(40-36\right)}\)
\(A:4=\frac{1}{2.3.4}+\frac{1}{2.3.4.5}-\frac{1}{2.3.4}+\frac{1}{3.4.5.6}-\frac{1}{2.3.4.5}+...+\frac{1}{37.38.39.40}-\frac{1}{36.37.38.39}\)
\(A:4=\frac{1}{37.38.39.40}\)
\(A=\frac{4}{37.38.39.40}\)
