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TD
2
3 tháng 7 2016
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x.\left(x+1\right):2}=\frac{399}{400}\)
\(2.\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{399}{400}\)
\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x.\left(x+1\right)}=\frac{399}{400}:2\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{399}{400}.\frac{1}{2}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{399}{800}\)
\(\frac{1}{x+1}=\frac{1}{2}-\frac{399}{800}\)
\(\frac{1}{x+1}=\frac{400}{800}-\frac{399}{800}\)
\(\frac{1}{x+1}=\frac{1}{800}\)
\(=>x+1=800\)
\(=>x=800-1=799\)
Vậy x = 799
Ủng hộ mk nha ^_-
TD
1
4 tháng 7 2016
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right):2}=\frac{399}{400}\)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{399}{400}\)
\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{399}{400}\)
\(2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{399}{400}\)
\(2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{399}{400}\)
\(2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{399}{400}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{399}{200}\)
\(\frac{1}{x+1}=\frac{-299}{200}\)
\(x+1=\frac{-200}{299}\)
\(x=\frac{-499}{299}\)
18 tháng 1 2017
a, |x - 1| = 4
\(\orbr{\begin{cases}x-1=4\\x-1=-4\end{cases}}\)
\(\orbr{\begin{cases}x=4+1\\x=-4+1\end{cases}}\)
\(\orbr{\begin{cases}x=5\\x=-3\end{cases}}\)
Vậy x = 4 hoặc x = -3
Các ý sau tương tự
XO
4 tháng 3 2020
Ta có : \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2016}\)
\(\Rightarrow2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2015}{2016}\)
\(\Rightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2015}{2016}\)
\(\Rightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2015}{2016}\)
\(\Rightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2015}{2016}\)
\(\Rightarrow1-\frac{2}{x+1}=\frac{2015}{2016}\)
\(\Rightarrow\frac{2}{x+1}=\frac{1}{2016}\)
=> x + 1 = 2016 . 2
=> x + 1 = 4032
=> x = 4031
Vậy x = 4031
LB
2
KN
25 tháng 2 2019
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2017}\)
\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2017}\)
\(\Leftrightarrow\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2017}\)
\(\Leftrightarrow\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}=\frac{2015}{2017}.\frac{1}{2}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2015}{4034}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2015}{4034}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2015}{4034}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2015}{4034}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{2}{4034}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2017}\)
\(\Leftrightarrow x+1=2017\)
\(\Leftrightarrow x=2017-1\)
\(\Leftrightarrow x=2016\)
Vậy x = 2016
25 tháng 2 2019
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2017}\)
\(\Rightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2017}\)
\(\Rightarrow2\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+....+\frac{1}{x\left(x+1\right)}\right)=\frac{2015}{2017}\)
\(\Rightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2015}{2017}\)
\(\Rightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2015}{2017}\)
\(\Rightarrow2\cdot\frac{x-1}{2\left(x+1\right)}=\frac{2015}{2017}\)
\(\Rightarrow\frac{x-1}{2x+2}=\frac{2015}{4034}\)
\(\Rightarrow4034x-4034=4030x+4030\)
\(\Rightarrow4034x-4030x=8064\)
\(\Rightarrow x=2016\)