Răspuns:
[tex]b=\frac{\sqrt{1}-\sqrt{2})1}{\sqrt{1}+\sqrt{2}} +\frac{\sqrt{2}-\sqrt{3})1}{\sqrt{2}+\sqrt{3}} +...+\frac{\sqrt{8}-\sqrt{9})1}{\sqrt{8}+\sqrt{9}} =\\=\frac{\sqrt{1}-\sqrt{2}}{1-2} +\frac{\sqrt{2}-\sqrt{3}}{2-3} +...+\frac{\sqrt{8}-\sqrt{9}}{8-9}=\\=\frac{\sqrt{1}-\sqrt{2}}{-1} +\frac{\sqrt{2}-\sqrt{3}}{-1} +...+\frac{\sqrt{8}-\sqrt{9}}{-1}=\\=-\sqrt{1}+\sqrt{2}-\sqrt{2}+\sqrt{3}+...+-\sqrt{8}+\sqrt{9} =-\sqrt{1}+\sqrt{9}=-1+3=2\\[/tex]
2∈N
Explicație pas cu pas:
