СРОЧНО НАДО!!!!!!!!!!!а=1/корень1+ корень 2 +1/ корень 2+ корень 3 +1 / корень 3+ корень 4 + ......1/ корень 2010+ корень 2011В числителе везде 1, а в знаменателе по два корня..например корень1+ корень 2

[latex]A = \sum\limits_{n = 1}^{2010} \frac{1}{\sqrt{n}+\sqrt{n+1}} = \frac{1}{\sqrt{1}+\sqrt{2}} + \frac{1}{\sqrt{2}+\sqrt{3}} + ... + \frac{1}{\sqrt{2010}+\sqrt{2011}} = \\\\ \frac{(\sqrt{2} - \sqrt{1})}{(\sqrt{1}+\sqrt{2})(\sqrt{2} - \sqrt{1})} + \frac{(\sqrt{3} - \sqrt{2})}{(\sqrt{2}+\sqrt{3})(\sqrt{3} - \sqrt{2})} + ... + \frac{(\sqrt{2011} - \sqrt{2010})}{(\sqrt{2010}+\sqrt{2011})(\sqrt{2011} - \sqrt{2010})} =[/latex] [latex]\frac{\sqrt{2} - \sqrt{1}}{2 - 1} + \frac{\sqrt{3} - \sqrt{2}}{3 -2} + ... + \frac{\sqrt{2011} - \sqrt{2010}}{2011 - 2010} = \\\\ \sqrt{2} - \sqrt{1} + \sqrt{3} - \sqrt{2} + ... + \sqrt{2010} -\sqrt{2009} + \sqrt{2011} - \sqrt{2010} =\\\\ \boxed{\sqrt{2011} - 1}[/latex]