Question

cum sar rezolva acest exercitiu ma poate ajuta cineva 

 1      +   1    + ..........+    1       = 2010
1x2       2x3               x(x+1)        2011

Answer 1

[tex] \frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} +...+ \frac{1}{x(x+1)} = \frac{2010}{2011}\\ \frac{1}{1}- \frac{1}{2} + \frac{1}{2} - \frac{1}{3}+...+ \frac{1}{x} - \frac{1}{x+1} =\frac{2010}{2011}\\ 1- \frac{1}{x+1}=\frac{2010}{2011}\\ \frac{1}{x+1}=1-\frac{2010}{2011}\\ \frac{1}{x+1}= \frac{1}{2011} \\ x+1=2011\\ x=2010[/tex]