x( 1/1*2 + 1/2*3 + 1/3*4 +...+1/2009*2010 + 1/2010*2011) =2010
1/1*2= 1/1 -1/2
1/2*3= 1/2 -1/3
1/3*4= 1/3 -1/4
......................................................
1/2009 *2010= 1/2009 -1/2010
1/2010*2011= 1/2010- 1/2011
S= 1/1- 1/2011 aducem la acelasi numitor
S= (2011-1)/2011
S=2010/2011
x* 2010/2011= 2010
2010x/2011=2010
x=2011*2010/2010
x=2011
