tìm số tự nhiên x,biết:1/3+1/6+...+1/x*(x+1)/2=2016/2018
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10 tháng 5 2017
1/2.(1/3+1/6+1/10+...+1/x(x+1))=1/2.2016/2018
1/6+1/12+1/20+...+1/x(x+1)=504/1009
1/2.3+1/3.4+1/4.5+...+1/x(x+1)=504/1009
1/2-1/3+1/3-1/4+1/4-1/5+...+1/x-1/x+1=504/1009
1/2-1/x+1=504/1009
x-1/2(x+1)=504/1009
-> 1009(x-1)=504.2(x+1)
1009x-1009=1008x+1008
1009x-1008x=1008+1009
->x=2017
LB
10 tháng 5 2017
\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right):2}=\frac{2016}{2018}\)
\(A=\frac{1}{2\left(2+1\right):2}+\frac{1}{3\left(3+1\right):2}+...+\frac{1}{x\left(x+1\right):2}\)
\(A=\frac{1}{2\left(2+1\right)}\cdot2+\frac{1}{3\left(3+1\right)}\cdot2+...+\frac{1}{x\left(x+1\right)}.2=\frac{2016}{2018}\)
\(A=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2016}{2018}\)
\(A=2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2016}{2018}\)
\(A=1-\frac{1}{x+1}=\frac{2016}{2018}\)
\(\Rightarrow\frac{1}{x+1}=1-\frac{2016}{2018}=\frac{1}{1009}\)
\(\Rightarrow x+1=1009\Rightarrow x=1008\)
MA
0
AA
3
22 tháng 4 2019
\(\Rightarrow\frac{2}{6}+\frac{2}{12}+...+\frac{2}{x.\left(x+1\right)}=\frac{2018}{2019}\)
\(\Rightarrow\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{x.\left(x+1\right)}=\frac{2018}{2019}\)
\(\Rightarrow2.\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{2018}{2019}\)
\(\Rightarrow2.\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2018}{2019}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{1009}{2019}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{4038}\)
\(\Rightarrow x+1=4038\)
\(\Rightarrow x=4037\)
Vậy \(x=4037\)
22 tháng 4 2019
\(\frac{1}{\frac{2.3}{2}}+\frac{1}{\frac{3.4}{2}}+...+\frac{2}{x.\left(x+1\right)}=\frac{2018}{2019}\)
\(\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{x.\left(x+1\right)}=\frac{2018}{2019}\)
\(2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}+\frac{1}{x+1}\right)=\frac{2018}{2019}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{1009}{2019}\)
\(\frac{1}{x+1}=\frac{1}{4038}\)
\(x=4037\)
TT
0
LT
4
13 tháng 5 2016
1/2+1/6+1/12+1/20+...+1/x(x+1)=2015/2016
1/1.2+1/2.3+1/3.4+.....+1/x.(x+1)=2015/2016
1-1/2+1/2-1/3+1/3-1/4+......+1/x-1/x+1=2015/2016
1-1/x-1=2015/2016
1/x+1=1-2015/2016
1/x+1=1/2016
=> x+1=2016
x=2016-1
x=2015
vậy x =2015
tích mình nha
HP
13 tháng 5 2016
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+.......+\frac{1}{x\left(x+1\right)}=\frac{2015}{2016}\)
=>\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.......+\frac{1}{x\left(x+1\right)}=\frac{2015}{2016}\)
=>\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+......+\frac{1}{x}-\frac{1}{x+1}=\frac{2015}{2016}\)
=>\(1-\frac{1}{x+1}=\frac{2015}{2016}\)
=>\(\frac{1}{x+1}=1-\frac{2015}{2016}=\frac{1}{2016}\)
=>x+1=2016
=>x=2015
Vậy x=2015
MV
11 tháng 5 2017
\(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+...+\dfrac{1}{x\cdot\left(x+1\right):2}=\dfrac{2016}{2018}\\ \dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{20}+...+\dfrac{2}{x\cdot\left(x+1\right)}=\dfrac{2016}{2018}\\ 2\cdot\left(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{x\cdot\left(x+1\right)}\right)=\dfrac{2016}{2018}\\ 2\cdot\left(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+...+\dfrac{1}{x\cdot\left(x+1\right)}\right)=\dfrac{2016}{2018}\\ 2\cdot\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{x}-\dfrac{1}{x+1}\right)=\dfrac{2016}{2018}:2\\ \dfrac{1}{2}-\dfrac{1}{x+1}=\dfrac{1008}{2018}\\ \dfrac{1}{x+1}=\dfrac{1}{2}-\dfrac{1008}{2018}\\ \dfrac{1}{x+1}=\dfrac{1}{2018}\\ \Leftrightarrow x+1=2018\\ x=2018-1\\ x=2017\)
LT
0
TN
2
21 tháng 4 2017
Ta phân tích :13=2+3+4
=> 1/2+1/3+1/4=13/12.
=> Ta có : 1/2016-x=1/2
=> Ta có 2016-x=2 =>x=2014
NT
7 tháng 8 2018
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THANKS
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Tìm số tự nhiên x biết
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\cdot\left(x+1\right):2}=\frac{2016}{2018}\)