[tex] \frac{1}{(k+1) \sqrt{k}+k \sqrt{k+1} } = \frac{1}{ \sqrt{k} \sqrt{k+1}( \sqrt{k+1} + \sqrt{k}) } =[/tex][tex] \frac{ \sqrt{k+1} - \sqrt{k} }{\sqrt{k} \sqrt{k+1}(k+1-k)}=\frac{\sqrt{k+1}}{\sqrt{k}\sqrt{k+1}} - \frac{\sqrt{k}}{\sqrt{k}\sqrt{k+1}} =\frac{1}{\sqrt{k}} - \frac{1}{\sqrt{k+1}} [/tex]
Cand sumam obtinem
[tex]1- \frac{1}{\sqrt{n+1}} [/tex] si trecand la limita ,limita este 1
