\(\frac{x-1}{2017}\)+ \(\frac{x-3}{2015}\)+ ...+ <...">
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8 tháng 1 2018

\(\frac{315-x}{101}+\frac{313-x}{103}+\frac{311-x}{105}+\frac{309-x}{107}=-4\)

\(\left(\frac{315-x}{101}+1\right)+\left(\frac{313-x}{103}+1\right)+\left(\frac{311-x}{105}+1\right)+\left(\frac{309-x}{107}+1\right)=0\)

\(\frac{416-x}{101}+\frac{416-x}{103}+\frac{416-x}{105}+\frac{416-x}{107}=0\)

\(\left(416-x\right).\left(\frac{1}{101}+\frac{1}{103}+\frac{1}{105}+\frac{1}{107}\right)=0\)

vì \(\frac{1}{101}+\frac{1}{103}+\frac{1}{105}+\frac{1}{107}\ne0\)nên 416 - x = 0

\(\Rightarrow x=416\)

28 tháng 7 2018

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2017}\)

\(\Rightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2017}\)

\(\Rightarrow2\times\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2015}{2017}\)

\(\Rightarrow2\times\left(\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2015}{2017}\)

\(\Rightarrow2\times\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2015}{2017}\)

\(\Rightarrow2\times\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2015}{2017}\)

\(\Rightarrow1-\frac{2}{x+1}=\frac{2015}{2017}\)

\(\Rightarrow\frac{2}{x+1}=\frac{2}{2017}\Rightarrow x+1=2017\Rightarrow x=2016\)

Vậy x = 2016

28 tháng 7 2018

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2017}\)

\(\Rightarrow2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2015}{2017}\)

\(\Rightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2015}{2017}\)

\(\Rightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2015}{2017}\)

\(\Rightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2015}{2017}\)

\(\Rightarrow1-\frac{2}{x+1}=\frac{2015}{2017}\)

\(\Rightarrow\frac{2}{x+1}=\frac{2}{2017}\)

\(\Rightarrow x+1=2017\)

\(\Rightarrow x=2016\)

Vậy \(x=2016\)

27 tháng 8 2016

x+4/2015 + x+3/2016 = x+2/2017 + x+1/2018

=> 1 + x+4/2015 + 1 + x+3/2016 = 1 + x+2/2017 + 1 + x+1/2018

=> x+2019/2015 + x+2019/2016 = x+2019/2017 + x+2019/2018

=> x+2019/2015 + x+2019/2016 - x+2019/2017 - x+2019/2018 = 0

=> (x + 2019).(1/2015 + 1/2016 - 1/2017 - 1/2018) = 0

Vì 1/2015 > 1/2017; 1/2016 > 1/2018

=> 1/2015 + 1/2016 - 1/2017 - 1/2018 khác 0

=> x + 2019 = 0

=> x = -2019

11 tháng 7 2016

\(\frac{x+1}{2015}+\frac{x+1}{2016}=\frac{x+1}{2017}+\frac{x+1}{2018}\)

\(\Rightarrow\frac{x+1}{2015}+\frac{x+1}{2016}-\frac{x+1}{2017}-\frac{x+1}{2018}=0\)

\(\left(x+1\right)\left(\frac{1}{2015}+\frac{1}{2016}-\frac{1}{2017}-\frac{1}{2018}\right)=0\)

\(\frac{1}{2015}+\frac{1}{2016}-\frac{1}{2017}-\frac{1}{2018}\ne0\)

\(\Rightarrow x+1=0\)

\(x=-1\)

11 tháng 7 2016

\(\Leftrightarrow\frac{x+1}{2015}+\frac{x+1}{2016}-\frac{x+1}{2017}-\frac{x+1}{2018}=0\)

\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{2015}+\frac{1}{2016}-\frac{1}{2017}-\frac{1}{2018}\right)=0\)

\(\Leftrightarrow x+1=0\) ( vì \(\frac{1}{2015}+\frac{1}{2016}-\frac{1}{2017}-\frac{1}{2018}\ne0\))

\(\Leftrightarrow x=-1\)

28 tháng 6 2015

\(\frac{315-x}{101}+\frac{313-x}{103}+\frac{311-x}{105}+\frac{309-x}{107}+4=0\)

\(\frac{315-x}{101}+1+\frac{313-x}{103}+1+\frac{311-x}{105}+1+\frac{309-x}{107}+1=0\)

\(\frac{315-x}{101}+\frac{101}{101}+\frac{313-x}{103}+\frac{103}{103}+\frac{311-x}{105}+\frac{105}{105}+\frac{309-x}{107}+\frac{107}{107}=0\)

\(\frac{416-x}{101}+\frac{416-x}{103}+\frac{416-x}{105}+\frac{416-x}{107}=0\)

\(\left(416-x\right)\left(\frac{1}{101}+\frac{1}{103}+\frac{1}{105}+\frac{1}{107}\right)=0\)

vì \(\frac{1}{101}+\frac{1}{103}+\frac{1}{105}+\frac{1}{107}\ne0\)nên

416-x=0

x=416

8 tháng 1 2018

bạn triều dâng làm đúng đấy .tớ cũng làm thế

2 tháng 12 2019

Có:\(\left(x+2020\right)\left(\frac{1}{2015}+\frac{1}{2016}+\frac{1}{2017}+\frac{1}{2018}\right)=0\)Mà \(\frac{1}{2015}+\frac{1}{2016}+\frac{1}{2017}+\frac{1}{2018}>0\)

=>x+2020=0<=>x=-2020

x/2015+x/2016+x/2017=0 =>x(1/2015+1/2016+1/2017+1/2018)=0 =>x=0

kick mk nha, chúc bn hok tốt!!

29 tháng 3 2018

\(\frac{x}{2015}+\frac{x}{2016}+\frac{x}{2017}-\frac{x}{2018}=0=>x\left(\frac{x}{2015}+\frac{x}{2016}+\frac{x}{2017}-\frac{x}{2018}\right)=0\)=> x 2015 1 + 2016 1 + 2017 1 − 2018 1 = 0 Dễ thấy biếu thức trong ngoặc khác 0 nên x = 0. 

4 tháng 7 2019

2/

a) Ta có x : 2 = y : 5

=> \(\frac{x}{2}=\frac{y}{5}\)\(x+y=21\).

Áp dụng tính chất dãy tỉ số bằng nhau ta được:

\(\frac{x}{2}=\frac{y}{5}=\frac{x+y}{2+5}=\frac{21}{7}=3.\)

\(\left\{{}\begin{matrix}\frac{x}{2}=3=>x=3.2=6\\\frac{y}{5}=3=>y=3.5=15\end{matrix}\right.\)

Vậy \(\left(x;y\right)=\left(6;15\right)\).

Chúc bạn học tốt!