Policzmy q.
[tex]q=\frac{a_3}{a_2}=\frac{\sqrt3-\sqrt2}{1}=\sqrt3-\sqrt2[/tex]
Zatem kolejne wyrazy to:
[tex]a_4=a_3*q=(\sqrt3-\sqrt2)(\sqrt3-\sqrt2)=(\sqrt3-\sqrt2)^2=3-2*\sqrt3*\sqrt2+2=5-2\sqrt6\\\\a_5=a_4*q=(5-2\sqrt6)(\sqrt3-\sqrt2)=5\sqrt3-5\sqrt2-2\sqrt{18}+2\sqrt{12}=\\=5\sqrt3-5\sqrt2-2\sqrt{9*2}+2\sqrt{4*3}=5\sqrt3-5\sqrt2-6\sqrt{2}+4\sqrt{3}=9\sqrt3-11\sqrt2[/tex]