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A=\(\frac{4}{11}-\frac{4}{13}+\frac{4}{13}-\frac{4}{15}+...+\frac{4}{99}-\frac{4}{101}\)
\(A=4\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{99}-\frac{1}{101}\right)\)
\(A=4.\left(\frac{1}{11}-\frac{1}{101}\right)\)
A=4. 90/1111=360/1111
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\(\frac{4}{9\times11}+\frac{4}{11\times13}+\frac{4}{13\times15}+...+\frac{4}{95\times97}+\frac{4}{97\times99}\)
\(=2\times\left(\frac{2}{9\times11}+\frac{2}{11\times13}+\frac{2}{13\times15}+...+\frac{2}{95\times97}+\frac{2}{97\times99}\right)\)
\(=2\times\left(\frac{11-9}{9\times11}+\frac{13-11}{11\times13}+\frac{15-13}{13\times15}+...+\frac{97-95}{95\times97}+\frac{99-97}{97\times99}\right)\)
\(=2\times\left(\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{95}-\frac{1}{97}+\frac{1}{97}-\frac{1}{99}\right)\)
\(=2\times\left(\frac{1}{9}-\frac{1}{99}\right)=\frac{20}{99}\)
4/9x11 + 4/11x13 + 4/13X15 + .............+ 4/95X97 + 4/97X99
=2 x (2/9x11 + 2/11x 13 + .........+2/95x97 + 2/97x99)
=2 x ( 1/9 - 1/11 + 1/11- 1/13 +...... + 1/97 - 1/99)
=2 x (1/9 - 1/99)
=2 x10/99
=20/99
Học tốt!
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Ta có :
\(G=\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{97.99}+\frac{2}{99.101}\)
\(G=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{97}-\frac{1}{99}+\frac{1}{99}-\frac{1}{101}\)
\(G=\left(\frac{1}{13}-\frac{1}{13}\right)+\left(\frac{1}{15}-\frac{1}{15}\right)+\left(\frac{1}{17}-\frac{1}{17}\right)+...+\left(\frac{1}{99}-\frac{1}{99}\right)+\left(\frac{1}{11}-\frac{1}{101}\right)\)
\(G=\frac{1}{11}-\frac{1}{101}\)
\(G=\frac{101}{1111}-\frac{11}{1111}\)
\(G=\frac{101-11}{1111}\)
\(G=\frac{90}{1111}\)
Vậy \(G=\frac{90}{1111}\)
Chúc bạn học tốt ~
\(G=\frac{2}{11\times13}+\frac{2}{13\times15}+\frac{2}{15\times17}+...+\frac{2}{97\times99}+\frac{2}{99\times101}\)
\(G=2\times\left(\frac{1}{11\times13}+\frac{1}{13\times15}+\frac{1}{15\times17}+...+\frac{1}{97\times99}+\frac{1}{99\times101}\right)\)
\(G=2\times\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{97}-\frac{1}{99}+\frac{1}{99}-\frac{1}{101}\right)\)
( GẠCH BỎ CÁC PHÂN SỐ GIỐNG NHAU TRONG NGOẶC)
\(G=2\times\left(\frac{1}{11}-\frac{1}{101}\right)\)
\(G=2\times\frac{90}{1111}\)
\(G=\frac{180}{1111}\)
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\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{11.13}+\frac{2}{13.15}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\)
\(=1-\frac{1}{15}\)
\(=\frac{14}{15}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{15\times14\times1}{13\times15+14}\)
\(=\frac{15\times\left(13+1\right)\times1}{13\times15+14}\)
\(=\frac{15\times13+15\times1}{13\times15+14}\)
\(=\frac{15\times13+15}{13\times15+14}\)
\(=\frac{15}{14}=1\frac{1}{14}\)
Học tốt !
![](https://rs.olm.vn/images/avt/0.png?1311)
15X14-1/13X15+14=15X13+15-1/13X15+14
=15X13+14/13X15+14
=1
k đúng cho mk nha
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