Question

tìm x thuộc N biết 1/3+1/6+1/10+...+2/x.(x+1)=1999/2001

Answer 1

\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+..+\frac{2}{x\left(x+1\right)}=\frac{1999}{2001}\)

\(2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+..+\frac{1}{x\left(x+1\right)}\right)=\frac{1999}{2001}\)

\(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}=\frac{1999}{2001}:2\)

\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+..+\frac{1}{x}-\frac{1}{x+1}=\frac{1999}{4002}\)

\(\frac{1}{2}-\frac{1}{x+1}=\frac{1999}{4002}\)

\(\frac{x+1-2}{2\left(x+1\right)}=\frac{1999}{4002}\Rightarrow\frac{x-1}{2\left(x+1\right)}=\frac{1999}{4002}\Leftrightarrow4002\left(x-1\right)=1999.2\left(x+1\right)\)

=> 4002x - 4002 = 3998x + 3998

=> 4002x - 3998x = 3998 + 4002

=> 4x               = 8000

=> x                  = 2000

Answer 2

!/3+1/6+1/10+...+2/x(x+1)=1999/2001

1/6+1/12+1/20+...+2/x(x+1)=1999/2001

2(1/6+1/12+1/20+...+1/x(x+1)=1999/2001

1/6+1/12+1/20+1/x(x+1)=1999/2001:2

1/6+1/12+1/20+...+1/x(x+1)=1999/4002

1/2x3+1/3x4+1/4x5+...+1/x(x+1)=1999/4002

1/2-1/3+1/3-1/4+1/4-1/5+...+1/x-1/x+1=1999/4002

1/2-1/x+1=1999/4002

1/x+1=1/2-1999/4002

1/x+1=1/2001

=>x+1=2001

=>x=2001-1

=x=2000

Vậy x=2000.

Answer 3

làm thế nào để ra 2/6 và 2/12 vậy