Question

Problema politehnica

Salut, ma puteti ajuta la problema numarul 259...? O sugestie de rezolvare caci nu-mi iasa deloc...?

Answer 1

$\frac{1}{(k+1) \sqrt{k}+k \sqrt{k+1} } = \frac{1}{ \sqrt{k} \sqrt{k+1}( \sqrt{k+1} + \sqrt{k}) } =$$\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}}$

Cand sumam obtinem

$1- \frac{1}{\sqrt{n+1}}$ si trecand la limita ,limita este 1