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C=5/2+5/6+5/18+5/54+5/162+5/486
C=1215/486+405/486+135/486+45/486+15/486+5/486
C=1215+405+135+45+15+5/486
C=1820/486=910/243
\(\dfrac{5}{2}+\dfrac{5}{6}+\dfrac{5}{18}+\dfrac{5}{54}+\dfrac{5}{162}+\dfrac{5}{486}\)
\(=\dfrac{5.243}{486}+\dfrac{5.81}{486}+\dfrac{5.27}{486}+\dfrac{5.9}{486}+\dfrac{5.3}{486}+\dfrac{5}{486}\)
\(=\dfrac{1215+405+135+45+15+5}{486}\)
\(=\dfrac{1820}{486}=\dfrac{910}{243}\)
Ta có : \(A=\frac{5}{2}+\frac{5}{6}+\frac{5}{18}+\frac{5}{54}+\frac{5}{162}+\frac{5}{468}\)
\(\Leftrightarrow\frac{1}{3}A=\frac{5}{6}+\frac{5}{18}+\frac{5}{54}+\frac{5}{162}+\frac{5}{468}+\frac{5}{1458}\)
\(\Leftrightarrow A-\frac{1}{3}A=\frac{5}{2}-\frac{5}{1458}\)
\(\Leftrightarrow\frac{2}{3}A=\frac{5}{2}-\frac{5}{1458}\)
\(\Leftrightarrow\frac{2}{3}A=\frac{1820}{729}\)
\(\Leftrightarrow A=\frac{1820}{729}.\frac{3}{2}=\frac{910}{243}\)
Đặt A=1/2+1/6+1/18+1/54+1/162+1/486 A*3=3/2+1/2+1/6+1/18+1/54+1/162 A*3-A={3/2+1/2+1/6+1/18+1/54+1/162}-{1/2+1/6+1/18+1/54+1/162+1/486} A*2=3/2-1/486 A*2={kết quả} =kết quả :2=A Vậy 1/2+1/6+/18+1/54+1/162+1/486=A
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