4/9x11 + 4/11x13 + 4/13X15 + .............+ 4/95X97 + 4/97X99
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Những câu hỏi liên quan
25 tháng 10 2023
\(\dfrac{4}{9\cdot11}+\dfrac{4}{11\cdot13}+...+\dfrac{4}{97\cdot99}\)
\(=2\left(\dfrac{2}{9\cdot11}+\dfrac{2}{11\cdot13}+...+\dfrac{2}{97\cdot99}\right)\)
\(=2\left(\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)
\(=2\cdot\left(\dfrac{1}{9}-\dfrac{1}{99}\right)\)
\(=2\cdot\dfrac{10}{99}=\dfrac{20}{99}\)
W
4
1 tháng 4 2017
2/11x13+2/13x15+2/15x17+...+2/97x99
=1/11-1/13+1/13-1/15+1/15-1/17+...+1/97-1/99
=1/11-1/99
=8/99
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
NP
7
NT
3
23 tháng 8 2016
=4x(\(\frac{1}{11x13}\)+\(\frac{1}{13x15}\)+.......+\(\frac{1}{99x101}\))
=4x(\(\frac{1}{11}\)-\(\frac{1}{13}\)+\(\frac{1}{13}\)-\(\frac{1}{15}\)+....+\(\frac{1}{99}\)-\(\frac{1}{101}\))
4x(\(\frac{1}{11}\)-\(\frac{1}{101}\))
=4x \(\frac{90}{1111}\)
=\(\frac{360}{1111}\)
23 tháng 8 2016
\(\frac{4}{11\times13}+\frac{4}{13\times15}+\frac{4}{15\times17}+...+\frac{4}{99\times101}\)
\(=\frac{4}{11}-\frac{4}{13}+\frac{4}{13}-\frac{4}{15}+\frac{4}{15}-\frac{4}{17}+...+\frac{4}{99}-\frac{4}{101}\)
\(=\frac{4}{11}-\frac{4}{101}\)
\(=\frac{360}{1111}\)
KV
16 tháng 3 2023
2/(7 × 9) + 2/(9 × 11) + 2/(11 × 13) + ... + 2/(97 × 99)
= 1/7 - 1/9 + 1/9 - 1/11 + 1/11 - 1/13 + ... + 1/97 - 1/99
= 1/7 - 1/99
= 92/693
NP
6
14 tháng 5 2019
\(B=\frac{4}{1\times3}+\frac{4}{3\times5}+...+\frac{4}{9\times11}+\frac{4}{11\times13}\)
\(=2\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+...+\frac{2}{9\times11}+\frac{2}{11\times13}\right)\)
\(=2\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=2\times\left(1-\frac{1}{13}\right)\)
\(=2\times\frac{12}{13}\)
\(=\frac{24}{13}\)
14 tháng 5 2019
B = \(\frac{4}{1.3}+\frac{4}{3.5}+...+\frac{4}{11.13}\)
\(=4\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{11.13}\right)\)
\(=4.\frac{1}{4}.\left(\frac{2}{1}-\frac{2}{3}+\frac{2}{3}-\frac{2}{5}+...+\frac{2}{11}-\frac{2}{13}\right)\)
\(=2-\frac{2}{13}=\frac{24}{13}\)
NH
3
PN
0
\(\frac{4}{9\times11}+\frac{4}{11\times13}+\frac{4}{13\times15}+...+\frac{4}{95\times97}+\frac{4}{97\times99}\)
\(=2\times\left(\frac{2}{9\times11}+\frac{2}{11\times13}+\frac{2}{13\times15}+...+\frac{2}{95\times97}+\frac{2}{97\times99}\right)\)
\(=2\times\left(\frac{11-9}{9\times11}+\frac{13-11}{11\times13}+\frac{15-13}{13\times15}+...+\frac{97-95}{95\times97}+\frac{99-97}{97\times99}\right)\)
\(=2\times\left(\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{95}-\frac{1}{97}+\frac{1}{97}-\frac{1}{99}\right)\)
\(=2\times\left(\frac{1}{9}-\frac{1}{99}\right)=\frac{20}{99}\)
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
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