Question

Va rog daca se poate acest exercitiu .
PS. *=înmultire
[..]=partea intreaga 

$[ \sqrt{1*2}]+ [\sqrt{2*3}]+...+ [ \sqrt{50*51}]=1275$

Answer 1

   
Partea intreaga a unui numar este:
 cel mai mare intreg nai mic decat numarul dat.

[tex]\displaystyle\\ n\times n\ \textless \ n(n+1) \ \textless \ (n+1)(n+1)\\\\ \sqrt{n\times n} \ \textless \ \sqrt{n(n+1)}\ \textless \ \sqrt{(n+1)(n+1)}\\\\ n \ \textless \ \sqrt{n(n+1)}\ \textless \ n+1\\\\ \Longrightarrow~~ \left[\sqrt{n(n+1)}\right]=n\\\\ \Longrightarrow [\sqrt{1*2}]+ [\sqrt{2*3}]+...+ [ \sqrt{50*51}]=1+2+\cdots+50 \\\\ 1+2+\cdots+50 = \frac{50\times 51}{2}=25\times 51=\boxed{\bf 1275}[/tex]