[tex]A=\frac{1}{\sqrt1+\sqrt2}+\frac{1}{\sqrt2+\sqrt3}+...+\frac{1}{\sqrt{99}+\sqrt{100}}\\
\boxed{\frac{1}{\sqrt{n}+\sqrt{n+1}}=\frac{\sqrt{n+1}-\sqrt{n}}{n+1-n}=\sqrt{n+1}-\sqrt{n}}\\
Aplicam\ si\ aici:\\
A=\sqrt2-1+\sqrt3-\sqrt2+\sqrt4-\sqrt3+...+\sqrt{100}-\sqrt{99}\\
Termenii\ se\ reduc\ si\ va\ ramane:\\
A=-1+\sqrt{100}\\
A=-1+10\\
A=9\in N\\
Q.E.D.[/tex]
