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Tìm x biết: 1/3.5 + 1/5.7 + 1/7.9 + ... + 1/x.(x+2) = 11/75
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T
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TT
1
TT
1
HT
27 tháng 8 2015
\(\left[\frac{12}{11}-\left(\frac{1}{2}+\frac{1}{44}\right)\right].\left(x-0,2\right)=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\)
\(\frac{25}{44}.\left(x-0,2\right)=\frac{1}{2}.\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{9.11}\right)\)
\(x-0,2=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}\right):\frac{25}{44}\)
\(x-\frac{1}{5}=\frac{22}{25}.\left(1-\frac{1}{11}\right)=\frac{22}{25}.\frac{10}{11}=\frac{4}{5}\)
\(x=\frac{4}{5}+\frac{1}{5}\)
\(x=1\)
UN
1
TM
18 tháng 4 2017
<=> 2/1.3 + 2/3.5 + 2/5.7 +....+ 2/(x+2)(x+4) = 100/101
<=> 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 +.....+ 1/x+2 - 1/x+4 = 100/101
<=> 1 - 1/x+4 = 100/101
<=> 1/x+4 = 1 - 100/101 <=> 1/x+4 = 1/101 <=> x+4 = 101 <=> x= 101 - 4 = 97
:)
TH
4
11 tháng 7 2015
1/3.5+1/5.7+1/7.9+...+1/(2x+1)(2x+3)=5/31
1/2(2/3.5+2/5.7+2/7.9+...+2/(2x+1)(2x+3))=5/31
1/3-1/5+1/5-1/7+1/7-1/9+...+1/2x+1-1/2x+3=5/31:1/2
1/3-1/2x+3=10/31
1/2x+3=1/3-10/31
1/2x+3=1/63
suy ra : 2x+3=63
2x=63-3
2x=60
x=60:2
x=30
vay x=30
nhớ **** cho mình nha
NV
1
S
26 tháng 7 2016
\(\text{Ta có:}\) \(\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\right).x=\frac{2}{3}\)
\(\Leftrightarrow2.\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\right).x=\frac{2}{3}.2\)
\(\Leftrightarrow\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right).x=\frac{4}{3}\)
\(\Leftrightarrow\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{9}-\frac{1}{11}\right).x=\frac{4}{3}\)
\(\Leftrightarrow\left(1-\frac{1}{11}\right)x=\frac{4}{3}\)
\(\Leftrightarrow\frac{10}{11}x=\frac{4}{3}\)
\(\Leftrightarrow x=\frac{4}{3}:\frac{10}{11}=\frac{22}{15}\)
TT
0
24 tháng 8 2019
\(\frac{1}{2}-\frac{1}{1.3}-\frac{1}{3.5}-\frac{1}{5.7}-\frac{1}{7.9}-\frac{1}{9.11}=\frac{4}{5}-x\)
<=> \(2.\frac{1}{2}-\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)=\frac{8}{5}-2x\)
<=> \(1-\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}\right)=\frac{8}{5}-2x\)
<=> \(1-\left(1-\frac{1}{11}\right)-\frac{8}{5}=-2x\)
<=> \(-\frac{83}{55}=-2x\)
<=> \(x=\frac{83}{110}\)
2 tháng 7 2015
1)
2/3.5+2/5.7+...+2/11.13+2/13.15+2/1.2+2/2.3+...+2/9.10
=(2/3.5+...2/13.15)+(2/1.2+...+2/9.10)
= (2/3-2/15)+ [2(1-1/10)]
=8/15+9/5
=7/3
2)
11/12+11/12.24+...+11/88.99
=11-1/9
=10/8/9
28 tháng 4 2021
d) Ta có: \(x+\dfrac{4}{5\cdot9}+\dfrac{4}{9\cdot13}+...+\dfrac{4}{41\cdot45}=\dfrac{-37}{45}\)
\(\Leftrightarrow x+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{41}-\dfrac{1}{45}=\dfrac{-37}{45}\)
\(\Leftrightarrow x+\dfrac{1}{5}-\dfrac{1}{45}=\dfrac{-37}{45}\)
\(\Leftrightarrow x=\dfrac{-37}{45}+\dfrac{1}{45}-\dfrac{1}{5}=\dfrac{-36}{45}-\dfrac{1}{5}=\dfrac{-4}{5}-\dfrac{1}{5}=-1\)
Vậy: x=-1
Ta có: \(\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\cdots+\frac{1}{x\left(x+2\right)}=\frac{11}{75}\)
=>\(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\cdots+\frac{2}{x\left(x+2\right)}=\frac{22}{75}\)
=>\(\frac13-\frac15+\frac15-\frac17+\cdots+\frac{1}{x}-\frac{1}{x+2}=\frac{22}{75}\)
=>\(\frac13-\frac{1}{x+2}=\frac{22}{75}\)
=>\(\frac{1}{x+2}=\frac13-\frac{22}{75}=\frac{3}{75}=\frac{1}{25}\)
=>x+2=25
=>x=23
x=−1.0±1.1257i