Question

1 supra 1ori 2 + 1 supra 2ori 3 + 1 supra 3ori 4 + ... +2010 supra 2011 ajutati-ma va rog nam stiut sa explic prea bine ori inseamna punctul din misloc.

Answer 1

$\frac{1}{1} - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \frac{1}{3}- \frac{1}{4} ...+ \frac{1}{2010} - \frac{1}{2011} =1- \frac{1}{2011} = \frac{2010}{2011}$

Answer 2

 $\frac{1}{1\cdot 2}+ \frac{1}{2\cdot 3}+...+ \frac{1}{2010\cdot 2011}= \frac{1}{1} -\frac{1}{2}+ \frac{1}{2}-\frac{1}{3}+...+ \frac{1}{2010}- \frac{1}{2011}(SUMA~~TELESCOPICA)\\ =1-\frac{1}{2011}=\frac{2011}{2011}-\frac{1}{2011}=\frac{2010}{2011}.$