Question

Tìm x:

1/3+ 1/6+ 1/10+ ...+1/x(x+1)= 2009/2011

Answer 1

Nhân cả 2 vế với 1/2 ta có:

1/6+ 1/12+ 1/20+... +1/x(x+1)=2009/4022

1/2.3+ 1/3.4+ 1/4.5+... +1/x(x+1)=2009/4022

1/2- 1/3+ 1/3-1/4+ 1/4- 1/5+...+1/x- 1/x+1=2009/4022

1/2- 1/x+1=2009/4022

x+1/2.(x+1)- 2/2.(x+1)=2009/4022

x+1-2/2.(x+1)=2009/4022

x-1/2.(x+1)=2009/4022

=>(x-1). 4022= 2009.2.(x+1)

 4022.x- 4022= 4018.x+ 4018

 4022.x-4018.x= 4018+ 4022

 x.(4022- 4018)= 8040

 x.4                = 8040

 x                   = 8040: 4

 x                   =2010