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\(=\frac{4}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+....+\frac{3}{80.83}\right)\)
\(=\frac{4}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+....+\frac{1}{80}-\frac{1}{83}\right)\)
\(=\frac{4}{3}.\left(\frac{1}{2}-\frac{1}{83}\right)\)
\(=\frac{54}{83}\)
\(\frac{4}{2\cdot5}+\frac{4}{5\cdot8}+............+\frac{4}{80\cdot83}\)
\(=4\left(\frac{1}{2\cdot5}+\frac{1}{5\cdot8}+............+\frac{4}{80\cdot83}\right)\)
\(=\frac{4}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...........+\frac{1}{80}-\frac{1}{83}\right)\)
\(=\frac{4}{3}\cdot\frac{81}{166}\)
\(=\frac{54}{83}\)
CHúc các bạn học tôt !!!!!!!!!!!!!!!!!!!
\(A=\frac{4}{2.5}+\frac{4}{5.8}+\frac{4}{8.11}+........+\frac{4}{65.68}\)
\(A=4\left(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+......+\frac{1}{65.68}\right)\)
\(A=\frac{4}{3}\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+..........+\frac{3}{65.68}\right)\)
\(A=\frac{4}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-.........-\frac{1}{68}\right)\)
\(A=\frac{4}{3}\left(\frac{1}{2}-\frac{1}{68}\right)\)
\(A=\frac{4}{3}\left(\frac{34}{68}-\frac{1}{68}\right)\)
\(A=\frac{4}{3}.\frac{33}{68}\)
\(A=\frac{11}{17}\)
\(A=\frac{4}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+.........+\frac{3}{98.101}\right)\)
\(=\frac{4}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+............+\frac{1}{98}-\frac{1}{101}\right)\)
\(=\frac{4}{3}.\left(\frac{1}{2}-\frac{1}{101}\right)\)
\(=\frac{4}{3}.\frac{99}{202}\)
\(=\frac{66}{101}\)
\(A=\frac{4}{2.5}+\frac{4}{5.8}+\frac{4}{8.11}+...+\frac{4}{98.101}\)
\(\frac{4}{3}A=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{98.101}\)
\(\frac{4}{3}A=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{101}\)
\(A=\left(\frac{1}{2}-\frac{1}{101}\right).\frac{3}{4}\)
\(A=\frac{99}{202}.\frac{3}{4}=\frac{297}{808}\)
A=1/3x(1/2x5+1/5x8+......+1/95x98)
A=1/3x(1/2-1/5+1/5-1/8+.........+1/95-1/98)
A=1/3x(1/2-1/98)
A=1/3x24/49
A=8/49
A =\(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{92.95}+\frac{1}{95.98}\)
A = \(\frac{1.3}{2.5.3}+\frac{1.3}{5.8.3}+\frac{1.3}{8.11.3}+...+\frac{1.3}{92.95.3}+\frac{1.3}{95.98.3}\)
A = \(\frac{1}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{92.95}+\frac{3}{95.98}\right)\)
A =\(\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{92}-\frac{1}{95}+\frac{1}{95}-\frac{1}{98}\right)\)
A =\(\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{98}\right)\)
A =\(\frac{1}{3}.\frac{97}{98}\)
A =\(\frac{97}{294}\)
\(A=\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+............+\frac{1}{92.95}+\frac{1}{95.98}\)
\(A=\frac{1}{3}\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+..........+\frac{3}{92.95}+\frac{3}{95.98}\right)\)
\(A=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-.............-\frac{1}{95}+\frac{1}{95}-\frac{1}{98}\right)\)
\(A=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{98}\right)\)
\(A=\frac{1}{3}\left(\frac{49}{98}-\frac{1}{98}\right)\)
\(A=\frac{1}{3}.\frac{48}{98}\)
\(A=\frac{8}{49}\)
Vậy A = \(\frac{8}{49}\)
Phân tích: 1/2.5 = 1/2 - 1/5
1/5.8 = 1/5 - 1/8
1/8.11 = 1/8 - 1/11
...
1/92.95 = 1/92 - 1/95
1/95.98 = 1/95 - 1/98
Ta có: 1/2 - 1/5 + 1/5 - 1/8 + 1/8 - 1/11 +...+ 1/92 - 1/95 + 1/95 - 1/98
3 = 3/2.5 + 3/5.8 + 3/8.11 + ...+ 3/92.95 + 3/95.98
3 = 1 - 1/2 + 1/2 - 1/5 + 1/5 - 1/8 + 1/8 - 1/11 +...+ 1/92 - 1/95 + 1/95 - 1/98
= 1 - 1/98
= 97/98 : 3 = 97/98 x 1/3 = (tự tính)
\(A=\frac{4}{1.2}+\frac{4}{2.3}+...+\frac{4}{2014.2015}\)
\(A=4\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2014.2015}\right)\)
\(A=4\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2014}-\frac{1}{2015}\right)\)
\(A=4\left(\frac{1}{1}-\frac{1}{2015}\right)\)
\(A=4\left(\frac{2015-1}{2015}\right)\)
\(A=4.\frac{2014}{2015}\)
... BẠN TỰ LÀM NỐT NHÉ!
A = 4/5.8 + 4/8.11 + ... + 4/305.308
A = 4. ( 1/5.8 + 1/8.11 + ... + 1/305 . 108 )
A = 4 x 1/3 ( 3/5.8 + 3/8.11 + ... + 3/105.108 )
A = 4/3 ( 1/5 - 1/8 + 1/8 - 1/11 + ... + 1/105 - 1/108 )
A = 4/3 ( 1/5 - 1/108 )
A = 4/3 . 103/540
A = 617/540
Vậy A = 617/540 !!
\(A=\frac{4}{5\cdot8}+\frac{4}{8\cdot11}+\frac{4}{11\cdot14}+...+\frac{4}{305\cdot308}\)
\(\frac{3}{4}A=\frac{3}{4}\left(\frac{4}{5\cdot8}+\frac{4}{8\cdot11}+...+\frac{4}{305\cdot308}\right)\)
\(\frac{3}{4}A=\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+...+\frac{3}{305\cdot308}\)
\(\frac{3}{4}A=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{305}-\frac{1}{308}\)
\(\frac{3}{4}A=\frac{303}{1540}\Rightarrow A=\frac{303}{1540}:\frac{3}{4}=\frac{101}{385}\)