\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2014}{2015}\)

\(\Rightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2014}{2015}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{1007}{2015}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{1007}{2015}\)

\(\Rightarrow\frac{1}{x+1}=\frac{1}{4030}\)

=>x+1=4030

=>x=4029

vậy x=4029

1/3+1/6+1/10+...+ 2/X(X+1) = 2014/2016

Lời giải:

$1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x(x+1)}=\frac{2014}{2015}$

$\frac{2}{2}+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+....+\frac{2}{x(x+1)}=\frac{2014}{2015}$

$\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x(x+1)}=\frac{1007}{2015}$

$1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{1007}{2015}$

$1-\frac{1}{x+1}=\frac{1007}{2015}$

$\frac{1}{x+1}=1-\frac{1007}{2015}=\frac{1008}{2015}$

$\Rightarrow x+1=\frac{2015}{1008}$
$\Rightarrow x=\frac{1007}{1008}$

\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{x(x+1)}=\frac{2014}{2015}$

=> (x+2020)/5=(x+2020)/6=(x+2020)/3+(x+2020)/2

=>(x+2020)(1/5+1/6)=(x+2020)(1/3+1/2)

Với x+2020=0=>x=-2020

Với x+2020 khác 0=>1/5+1/6=1/3+1/2 ,vô lí 

Vậy x=-2020

tk mk , mk tk 

\(\frac{3+5+7+...+2015}{2+4+6+...+2014}+x=1\)

\(\frac{\left(3+2015\right).\left[\left(2015-3\right):2+1\right]:2}{\left(2+2014\right).\left[\left(2014-2\right):2+1\right]:2}+x=1\)

\(\frac{1016063}{1015056}+x=1\)

\(x=1-\frac{1016063}{1015056}\)

\(x=-\frac{1}{1008}\)

1,-2015

2,50

3,-2015

thiện xạ 5a3 có thể giải chi tiết ra đc k? Mk cần cách lm

2) 1+2+3+...+x=1275

  Có SSH là: (x+1):1+1=x(SH)

  => (x+1).x:2=1275

=>(x+1).x=1275.2

=>(x+1).x=2550

=>(x+1).x=51.50

=>x=50

3) |x+2015|+|x+2016|=1

Ta thấy  |x+2015| và  |x+2016| > hoặc = 0 với mọi x

=> 1= 0+1=1+0

+) x+2015=0=>x=-2015

     x+2016=1=>x=-2015

+) x+2015=1=>x=-2014

     x+2016=0=> x=-2016

Vậy xE{...}

1/3 = 2/6 = 2/(2x3) = 2/2 - 2/3
1/6 = 2/12 = 2/(3x4) = 2/3 - 2/4
...
2/x(x + 1) = 2/x - 2/(x +1)
Do đó: 
1/3 + 1/6 + ... + 2/x(x+1) = 2/2 - 2/3 + 2/3 - 2/4 + ... +2/x - 2/(x + 1) = 2/2 - 2/(x+1)
suy ra 1 - 2/(x + 1) = 2013/2014

x= 4027

1/3 = 2/6 = 2/(2x3) = 2/2 - 2/3 1/6 = 2/12 = 2/(3x4) = 2/3 - 2/4 ... 2/x(x + 1) = 2/x - 2/(x +1) Do đó: 1/3 + 1/6 + ... + 2/x(x+1) = 2/2 - 2/3 + 2/3 - 2/4 + ... +2/x - 2/(x + 1) = 2/2 - 2/(x+1) suy ra 1 - 2/(x + 1) = 2013/2014 x= 4027