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\(\frac{1}{9x11}+\frac{1}{11x13}+\frac{1}{13x15}+.......+\frac{1}{97x99}\)
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Những câu hỏi liên quan
NM
1
15 tháng 4 2016
\(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}+\frac{2}{11\cdot13}+\frac{2}{13\cdot15}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\)
\(=\frac{1}{3}-\frac{1}{15}\)
\(=\frac{4}{15}\)
Chúc bn hok giỏi !!!!!!!!! ^_^
25 tháng 10 2023
\(\dfrac{4}{9\cdot11}+\dfrac{4}{11\cdot13}+...+\dfrac{4}{97\cdot99}\)
\(=2\left(\dfrac{2}{9\cdot11}+\dfrac{2}{11\cdot13}+...+\dfrac{2}{97\cdot99}\right)\)
\(=2\left(\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)
\(=2\cdot\left(\dfrac{1}{9}-\dfrac{1}{99}\right)\)
\(=2\cdot\dfrac{10}{99}=\dfrac{20}{99}\)
TT
2
5 tháng 6 2018
\(A=\frac{1}{11.13}+\frac{1}{13.15}+..+\frac{1}{19.21}\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+..+\frac{1}{19}-\frac{1}{21}\right)\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{11}-\frac{1}{21}\right)\)
5 tháng 6 2018
\(A=\frac{1}{11\cdot13}+\frac{1}{13\cdot15}+...+\frac{1}{19\cdot21}\)
\(2A=\frac{2}{11\cdot13}+\frac{2}{13\cdot15}+...+\frac{2}{19\cdot21}\)
\(2A=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\)
\(2A=\frac{1}{11}-\frac{1}{21}+0+...+0\)
\(2A=\frac{10}{231}\)
\(A=\frac{5}{231}\)
29 tháng 6 2017
\(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}+\frac{2}{1.2}+\frac{2}{2.3}+...+\frac{2}{9.10}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}+2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(=\frac{1}{3}-\frac{1}{15}+2\left(1-\frac{1}{10}\right)\)
\(=\frac{4}{15}+\frac{9}{5}\)
\(=\frac{31}{15}\)
B
15 tháng 9 2020
Bài làm :
Ta có :
\(\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{13\times15}+\frac{2}{1\times2}+\frac{2}{2\times3}+...+\frac{2}{9\times10}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}+2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(=\frac{1}{3}-\frac{1}{15}+2\left(1-\frac{1}{10}\right)\)
\(=\frac{31}{15}\)
NA
2
CL
24 tháng 4 2016
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
ND
1
NN
Nguyễn Ngọc Anh Minh
CTVHS
VIP
28 tháng 12 2021
\(=\frac{7-5}{5x7}+\frac{9-7}{7x9}+\frac{11-9}{9x11}+...+\frac{15-13}{13x15}=\)
\(=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{13}-\frac{1}{15}=\frac{1}{5}-\frac{1}{15}=\frac{2}{15}\)
CC
2
DD
Đoàn Đức Hà
Giáo viên
25 tháng 5 2021
\(\frac{4}{9\times11}+\frac{4}{11\times13}+\frac{4}{13\times15}+...+\frac{4}{95\times97}+\frac{4}{97\times99}\)
\(=2\times\left(\frac{2}{9\times11}+\frac{2}{11\times13}+\frac{2}{13\times15}+...+\frac{2}{95\times97}+\frac{2}{97\times99}\right)\)
\(=2\times\left(\frac{11-9}{9\times11}+\frac{13-11}{11\times13}+\frac{15-13}{13\times15}+...+\frac{97-95}{95\times97}+\frac{99-97}{97\times99}\right)\)
\(=2\times\left(\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{95}-\frac{1}{97}+\frac{1}{97}-\frac{1}{99}\right)\)
\(=2\times\left(\frac{1}{9}-\frac{1}{99}\right)=\frac{20}{99}\)
25 tháng 5 2021
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!
31 tháng 8 2016
\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{11.13}+\frac{2}{13.15}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\)
\(=1-\frac{1}{15}\)
\(=\frac{14}{15}\)
NT
1
22 tháng 4 2020
\(\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}+\frac{2}{11\cdot13}+\frac{2}{13\cdot15}\)
\(=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+....-\frac{1}{15}\)
\(=\frac{1}{5}-\frac{1}{15}=\frac{2}{15}\)
Mọi người giúp mik với mik đang cần gấp
\(=\frac{1}{2}\times\left(\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+...+\frac{1}{97}-\frac{1}{99}\right)\)
\(=\frac{1}{2}\times\left(\frac{1}{9}-\frac{1}{99}\right)\)
\(=\frac{1}{2}\times\frac{10}{99}\)
\(=\frac{5}{99}\)