Bài 1: Tìm x biết
x + 3/5.8 + 3/8.11 + 3/11.14 + ... + 3/32.35 = -2/7
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LT
1
17 tháng 4 2019
Dat A=3/5.8 +3/8.11 +.........+3/32.35
A=1/5-1/8+1/8-1/11+1/11-1/14+.............+1/32-1/35
A=1/5-1/35
A=6/35
=>x+6/35=-29/35
=>x=-29/35-6/35
=>x=-1
NT
1
BT
1
DV
0
TB
2
S
27 tháng 2 2017
\(\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+...+\frac{1}{x\left(x+3\right)}=\frac{101}{1540}\)
\(\Rightarrow\frac{1}{3}\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{x}-\frac{1}{x+3}\right)=\frac{101}{1540}\)
\(\Rightarrow\frac{1}{3}\left(\frac{1}{5}-\frac{1}{x+3}\right)=\frac{101}{1540}\)
\(\Rightarrow\frac{1}{5}-\frac{1}{x+3}=\frac{101}{1540}:\frac{1}{3}\)
\(\Rightarrow\frac{1}{5}-\frac{1}{x+3}=\frac{303}{1540}\)
\(\Rightarrow\frac{1}{x+3}=\frac{1}{5}-\frac{303}{1540}\)
=> \(\frac{1}{x+3}=\frac{1}{308}\)
=> x + 3 = 308
=> x = 308 - 3
=> x = 305
DK
0
BM
1
VD
3 tháng 4 2018
x.\(\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}\right)=-1\frac{3}{5}\)
x.\(\left(\frac{5-2}{2.5}+\frac{8-5}{5.8}+\frac{11-8}{8.11}+\frac{14-11}{11.14}+\frac{17-14}{14.17}\right)=\frac{-8}{5}\)
x.\(\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\right)=\frac{-8}{5}\)
x.\(\left(\frac{1}{2}-\frac{1}{17}\right)=\frac{-8}{5}\)
x.\(\left(\frac{17}{34}-\frac{2}{34}\right)=\frac{-8}{5}\)
x.\(\frac{15}{34}=\frac{-8}{5}\)
x\(=\frac{-8}{5}:\frac{15}{34}\)
x\(=\frac{-8}{5}.\frac{34}{15}\)
x\(=\frac{-272}{75}\)
Vậy x\(=\frac{-272}{75}\)
LM
1
Đặt \(A=\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{32.35}\)
\(A=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{32}-\frac{1}{35}\)
\(A=\frac{1}{5}-\frac{1}{35}=\frac{6}{35}\)
\(\Rightarrow x+\frac{6}{35}=-\frac{2}{7}\Rightarrow x=-\frac{2}{7}-\frac{6}{35}=-\frac{16}{35}\)