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\(A=\frac{4}{2.5}+\frac{4}{5.8}+...+\frac{4}{98.101}\)
\(A=\frac{4}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+...+\frac{3}{98.101}\right)\)
\(A=\frac{4}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{101}\right)\)
\(A=\frac{4}{3}.\left(\frac{1}{2}-\frac{1}{101}\right)\)
\(A=\frac{4}{3}.\frac{99}{102}=\frac{66}{101}\)
\(\text{Ta có: }\) \(A=\frac{4}{2.5}+\frac{4}{5.8}+...+\frac{4}{98.101}\)
\(=\frac{4.3}{2.5.3}+\frac{4.3}{5.8.3}+\frac{4.3}{8.11.3}+.....+\frac{4.3}{98.101.3}\)
\(=\frac{4}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+.....+\frac{3}{98.101}\right)\)
\(=\frac{4}{3}.\left(\frac{1}{2}-\frac{1}{101}\right)\)
\(=\frac{4}{3}.\frac{99}{102}=\frac{66}{101}\)
#)Giải :
\(A=\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{98.101}\)
\(\Rightarrow3A=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{99.101}\)
\(\Rightarrow3A=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{99}-\frac{1}{101}\)
\(\Rightarrow3A=\frac{1}{2}-\frac{1}{101}\)
\(\Rightarrow3A=\frac{99}{202}\)
\(\Leftrightarrow A=\frac{33}{202}\)
\(A=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{101}\right)\)
\(A=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{101}\right)\)
\(A=\frac{1}{3}.\frac{99}{202}=\frac{33}{202}\)
S = 4/2.5 + 4/5.8 + 4/8.11 + ... + 4/65.48
S = 4/3 . ( 3/2.5 + 3/5.8 + 3/8.11 + ... + 3/65.68 )
S = 4/3 . ( 1/2 - 1/5 + 1/5 - 1/8 + 1/8 - 1/11 + ... + 1/65 - 1/68 )
S = 4/3 . ( 1/2 - 1/68 )
S = 4/3 . 33/68
S = 11/17
\(A=\frac{4}{2.5}+\frac{4}{5.8}+\frac{4}{8.11}+...+\frac{4}{65.68}\)
\(A=\frac{4}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{65.68}\right)\)
\(A=\frac{4}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{65}-\frac{1}{68}\right)\)
\(A=\frac{4}{3}.\left[\frac{1}{2}+\left(\frac{1}{5}-\frac{1}{5}\right)+\left(\frac{1}{8}-\frac{1}{8}\right)+...+\left(\frac{1}{65}-\frac{1}{65}\right)-\frac{1}{68}\right]\)
\(A=\frac{4}{3}.\left[\frac{1}{2}-\frac{1}{68}\right]\)
\(A=\frac{4}{3}.\frac{33}{68}\)
\(A=\frac{11}{17}\)
~ Hok tốt ~
\(A=\frac{4}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+....+\frac{1}{65}-\frac{1}{68}\right)\)
\(=\frac{4}{3}\left(\frac{1}{2}-\frac{1}{68}\right)\)
\(=\frac{4}{3}\times\frac{33}{68}=\frac{11}{17}\)
\(\frac{4}{2\cdot5}\)+\(\frac{4}{5\cdot8}\)+\(\frac{4}{8\cdot11}\)+.......+\(\frac{4}{8\cdot83}\)=\(\frac{4}{3}\) (\(\frac{3}{2\cdot5}\)+\(\frac{3}{5\cdot8}\) +......+\(\frac{3}{80\cdot83}\) )
=\(\frac{4}{3}\) (\(\frac{1}{2}\) -\(\frac{1}{5}\) +\(\frac{1}{5}\) -\(\frac{1}{8}\) +..........+\(\frac{1}{80}\) -\(\frac{1}{83}\) )
=\(\frac{4}{3}\) (\(\frac{1}{2}\) -\(\frac{1}{83}\) )
=\(\frac{4}{3}\)*\(\frac{81}{166}\)
=\(\frac{54}{83}\)
\(A=\frac{4}{2.5}+\frac{4}{5.8}+\frac{4}{8.11}+.........+\frac{4}{65.68}\)
\(A=4\left(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+.........+\frac{1}{65.68}\right)\)
\(A=\frac{4}{3}\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+..........+\frac{3}{65.68}\right)\)
\(A=\frac{4}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-...........-\frac{1}{65}-\frac{1}{68}\right)\)
\(A=\frac{4}{3}\left(\frac{1}{2}-\frac{1}{68}\right)\)
\(A=\frac{4}{3}\left(\frac{34}{68}-\frac{1}{68}\right)\)
\(A=\frac{4}{3}\left(\frac{33}{68}\right)\)
\(A=\frac{11}{17}\)
Vậy A = \(\frac{11}{17}\)
Chúc bạn học tốt!
Gọi biểu thức đó là A
Ta có: \(A=\frac{4}{2.5}+\frac{4}{5.8}+\frac{4}{8.11}+...+\frac{4}{17.20}\)
\(A:4.3=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{17.20}\)
\(A:4.3=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{17}-\frac{1}{20}\)
\(A:4.3=\frac{1}{2}-\frac{1}{20}\)
\(A:4.3=\frac{9}{20}\)
\(A=\frac{3}{5}\)
\(=\frac{4}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+....+\frac{3}{80.83}\right)\)
\(=\frac{4}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+....+\frac{1}{80}-\frac{1}{83}\right)\)
\(=\frac{4}{3}.\left(\frac{1}{2}-\frac{1}{83}\right)\)
\(=\frac{54}{83}\)
\(\frac{4}{2\cdot5}+\frac{4}{5\cdot8}+............+\frac{4}{80\cdot83}\)
\(=4\left(\frac{1}{2\cdot5}+\frac{1}{5\cdot8}+............+\frac{4}{80\cdot83}\right)\)
\(=\frac{4}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...........+\frac{1}{80}-\frac{1}{83}\right)\)
\(=\frac{4}{3}\cdot\frac{81}{166}\)
\(=\frac{54}{83}\)
CHúc các bạn học tôt !!!!!!!!!!!!!!!!!!!
\(A=\frac{4}{2.5}+\frac{4}{5.8}+\frac{4}{8.11}+........+\frac{4}{65.68}\)
\(A=4\left(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+......+\frac{1}{65.68}\right)\)
\(A=\frac{4}{3}\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+..........+\frac{3}{65.68}\right)\)
\(A=\frac{4}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-.........-\frac{1}{68}\right)\)
\(A=\frac{4}{3}\left(\frac{1}{2}-\frac{1}{68}\right)\)
\(A=\frac{4}{3}\left(\frac{34}{68}-\frac{1}{68}\right)\)
\(A=\frac{4}{3}.\frac{33}{68}\)
\(A=\frac{11}{17}\)
\(A=\frac{4}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+.........+\frac{3}{98.101}\right)\)
\(=\frac{4}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+............+\frac{1}{98}-\frac{1}{101}\right)\)
\(=\frac{4}{3}.\left(\frac{1}{2}-\frac{1}{101}\right)\)
\(=\frac{4}{3}.\frac{99}{202}\)
\(=\frac{66}{101}\)
\(A=\frac{4}{2.5}+\frac{4}{5.8}+\frac{4}{8.11}+...+\frac{4}{98.101}\)
\(\frac{4}{3}A=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{98.101}\)
\(\frac{4}{3}A=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{101}\)
\(A=\left(\frac{1}{2}-\frac{1}{101}\right).\frac{3}{4}\)
\(A=\frac{99}{202}.\frac{3}{4}=\frac{297}{808}\)