Question

Am nevoie de ajutor repede !​

Answer 1

$\frac{\sqrt2-1}{\sqrt2}+\frac{\sqrt3-\sqrt2}{\sqrt6}+\frac{\sqrt4-\sqrt3}{\sqrt12}+...+\frac{\sqrt64-\sqrt63}{\sqrt4032}=$
$(\frac{1}{1}-\frac{1}{\sqrt2})+(\frac{1}{\sqrt2}-\frac{1}{\sqrt3})+(\frac{1}{\sqrt3}-\frac{1}{\sqrt4})+...+(\frac{1}{\sqrt63}-\frac{1}{\sqrt64})=$
$\frac{1}{1}-\frac{1}{\sqrt2}+\frac{1}{\sqrt2}-\frac{1}{\sqrt3}+\frac{1}{\sqrt3}-\frac{1}{\sqrt4}+...+\frac{1}{\sqrt63}-\frac{1}{\sqrt64}=$
$1-\frac{1}{8}=\frac{7}{8}$