Đáp án:
x=2008
Giải thích các bước giải:
1/3+1/6+1/10+...2/x(x+1)=2007/2009
1/2[1/3+1/6+1/10+...2/x(x+1)]=2007/2009.1/2
1/6+1/12+1/20+...+1/x(x+1)=2007/4018
1/2.1/3+1/3.1/4+1/4.1/5+...+1/x.1/x+1=2007/4018
1/2-1/3+1/3-1/4+1/4-1/5+...+1/x-1/x+1=2007/4018
1/2-1/x+1=2007/4018
1/x+1=1/2-2007/4018
1/x+1=2009/4018-2007/4018
1/x+1=2/4018
1/x+1=1/2009
=>x+1=2009
x =2009-1
Vậy x=2008
