Tìm x biết: (1/2.5+1/5.8+1/8.11+...+1/65.68)x-7/34=19/68
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6 tháng 3 2016
đặt \(\left(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+....+\frac{1}{65.68}\right)\)là A
Ax=\(\frac{19}{68}+\frac{7}{34}=\frac{33}{68}\)
3A=\(3.\left(\frac{1}{2.5}+\frac{1}{5.8}+\frac{11}{8.11}+...+\frac{1}{65.68}\right)\)
3A=\(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{65.68}\)
3A=\(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{65}-\frac{1}{68}\)
3A=\(\frac{1}{2}-\frac{1}{68}=\frac{33}{68}\)
A=33/68:3=11/68
\(\Rightarrow\)33/68:11/68=3
vậy x= 3
23 tháng 2 2017
bai 1:\(\frac{1}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{65}-\frac{1}{68}\right)x-\frac{7}{34}=\frac{19}{68}\)
=\(\frac{1}{3}\left(\frac{1}{2}-\frac{1}{68}\right)x-\frac{7}{34}=\frac{19}{68}\)
\(\Rightarrow\)x=3
bai2:từ giả thiết \(\frac{ab}{bc}=\frac{a}{c}=\frac{-1}{2}va\frac{ab}{ac}=\frac{b}{c}=\frac{3}{4}\)
hay \(\frac{a}{-2}=\frac{b}{3}=\frac{c}{4}\)
\(\Rightarrow\)\(\left(\frac{a}{-2}\right)^2=\frac{a}{-2}\times\frac{b}{3}=\frac{-6}{-6}=1\)
a=-2 (a<0)
\(\Rightarrow\)a=-2,b=3,c=4
NT
2
14 tháng 2 2016
\(\Rightarrow A=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+....+\frac{1}{65}-\frac{1}{68}\right)\)
\(\Rightarrow A=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{68}\right)=\frac{1}{2}\left(\frac{34}{68}-\frac{1}{68}\right)=\frac{1}{2}.\frac{33}{68}=\frac{33}{136}\)
24 tháng 7 2021
Ta có: \(A=\dfrac{4}{2\cdot5}+\dfrac{4}{5\cdot8}+...+\dfrac{4}{65\cdot68}\)
\(=\dfrac{4}{3}\cdot\left(\dfrac{3}{2\cdot5}+\dfrac{3}{5\cdot8}+...+\dfrac{3}{65\cdot68}\right)\)
\(=\dfrac{4}{3}\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+...+\dfrac{1}{65}-\dfrac{1}{68}\right)\)
\(=\dfrac{4}{3}\left(\dfrac{1}{2}-\dfrac{1}{68}\right)\)
\(=\dfrac{4}{3}\cdot\dfrac{33}{68}=\dfrac{11}{17}\)
NT
1
29 tháng 3 2018
\(\dfrac{12}{2.5}+\dfrac{12}{5.8}+.......+\dfrac{12}{65.68}\)
\(=4\left(\dfrac{3}{2.5}+\dfrac{3}{5.8}+......+\dfrac{3}{65.68}\right)\)
\(=4\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+.......+\dfrac{1}{65}-\dfrac{1}{68}\right)\)
\(=4\left(\dfrac{1}{2}-\dfrac{1}{68}\right)\)
\(=4.\dfrac{33}{68}=\dfrac{33}{17}\)
T
29 tháng 3 2018
Dễ quá! Vì mình là một CTV bên Học toán với OnlineMath nên bài này easy!! :")))
\(\dfrac{12}{2.5}+\dfrac{12}{5.8}+\dfrac{12}{8.11}+...+\dfrac{12}{65.68}\)
\(\Leftrightarrow4\left(\dfrac{2}{2.5}+\dfrac{2}{5.8}+\dfrac{2}{8.11}+...+\dfrac{2}{65.68}\right)\)
\(\Leftrightarrow4\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{65}-\dfrac{1}{68}\right)\)
\(=4\left(1-\dfrac{1}{68}\right)=4.\dfrac{67}{68}=\dfrac{67}{17}\)
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