1/2013.x+1+1/2+1/6+1/12+...+1/2012.2013=2

1/2013.x+1+1/1.2+1/2.3+1/3.4+...+1/2012.2013=2

1/2013.x+1+1-1/2+1/2-1/3+1/3-1/4+...+1/2012-1/2013=2

1/2013.x+2-1/2013=2

1/2013.x                   =2-2+1/2013

1/2013.x                   =1/2013

=>2013.x=2013

=> x=1

\(\Rightarrow\frac{1}{2013.x}+1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{2012}-\frac{1}{2013}=2\)

\(\Rightarrow\frac{1}{2013.x}+2-\frac{1}{2013}=2\)

\(\Rightarrow\frac{1}{2013.x}=2-2+\frac{1}{2013}\)

\(\Rightarrow\frac{1}{2013.x}=\frac{1}{2013}\)

\(\Rightarrow2013.x=2013\)

\(\Rightarrow x=1\)

\(\frac{1}{2013}x+1+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{2012.2013}=2\)

\(\frac{1}{2013}x+1+(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2012.2013})=2\)

\(\frac{1}{2013}x+1+\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2012}-\frac{1}{2013}\right)=2\)

\(\frac{1}{2013}x+1+\left(1-\frac{1}{2013}\right)=2\)

\(\frac{1}{2013}x+1+1-\frac{1}{2013}=2\)

\(\frac{1}{2013}x-\frac{1}{2013}+2=2\)

\(\frac{1}{2013}.\left(x-1\right)=2-2\)

\(\frac{1}{2013}.\left(x-1\right)=0\)

=> x - 1 = 0

x = 1

\(\frac{1}{2013}x+1+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{2012.2013}=2\)

\(\frac{1}{2013}x+\left(1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2012.2013}\right)=2\)

\(\frac{1}{2013}x+\left(1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2012}-\frac{1}{2013}\right)=2\)

\(\frac{1}{2013}x+\left(1-\frac{1}{2013}\right)=2\)

\(\frac{1}{2013}x+\frac{2012}{2013}=2\)

\(\frac{1}{2013}x=2-\frac{2012}{2013}\)

\(\frac{1}{2013}x=\frac{2014}{2013}\)

\(x=\frac{2014}{2013}:\frac{1}{2013}\)

=> x=2014

Bài này cực khó

bài này khó quá

2/6+2/12+2/20+...+2/x(x+2)=2013/2015

2(1/2.3+1/3.4+...+1/x(x+1))=2013/2015

2(1/2-1/3+1/3-1/4+...+1/x-1/x+1)=2013/2015

2(1/2-1/x+1)=2013/2015

1/2-1/x+1=2013/2015:2

1/2-1/x+1=2013/4030

1/x+1=1/2-2013/4030

1/x+1=1/2015

Suy ra x+1=2015

x=2014

Vậy x=2014

Ta có : x + (x + 1) + (x + 2) + .... + (x + 2012) = 2012.2013

<=> (x + x + x + ..... + x) + (1 + 2 + .... + 2012)  = 2012.2013

<=> 2013x + \(\frac{2012.2013}{2}\) = 2012.2013

<=> 2013x = 2012.2013 - \(\frac{2012.2013}{2}\)

<=> 2013x = 2025078

mình trả lời bài 1 thôi nhé :

Gọi biểu thức trên là A.

Theo bài ra ta có:A=1/1.6+1/6.11+1/11.16+...+1/(5n+1)+1/(5n+6)

                           =1/5(1-1/6+1/6-1/11+1/11-1/16+...+1/5n+1-1/5n+6)

                           =1/5(1-1/5n+6)

                           =1/5( 5n+6/5n+6-1/5n+6)

                           =1/5(5n+6-1/5n+6)

                           =1/5.5n+5/5n+6

                           =n+1/5n+6

                           =ĐIỀU PHẢI CHỨNG MINH

x- 20/11.13 - 20/13.15 - 20/13.15 - 20/15.17 -...- 20/53.55=3/11

x-10.(2/11.13+2/13.15+2/15.17+...+2/53.55=3/11

x-10.(1/11-1/13+1/13-1/15+1/15-1/17+...+1/53-1/55)=3/11

x-10.(1/11-1/55)=3/11

x-10.4/55=3/11

x-8/11=3/11

x = 3/11+8/11

x=11/11=1

****

\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2013}{2015}\)

\(2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2013}{2015}\)

\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2013}{2015}:2\)

\(\frac{1}{2}-\frac{1}{x+1}=\frac{2013}{4030}\)

tự làm tiếp nhé mk ăn cơm đã