Răspuns:
[tex]\dfrac{1}{\sqrt{10}+\sqrt{9}} +\dfrac{1}{\sqrt{11}+\sqrt{10}}+ \dfrac{1}{\sqrt{12}+\sqrt{11}} +...+\dfrac{1}{\sqrt{623}+\sqrt{622}}+\dfrac{1}{\sqrt{624}+\sqrt{623}}+\dfrac{1}{\sqrt{625}+\sqrt{624}}=\sqrt{10}-\sqrt{9}+\sqrt{11}-\sqrt{10}+\sqrt{12}-\sqrt{11} +...+ \sqrt{623}-\sqrt{622}+\sqrt{624}-\sqrt{623}+\sqrt{625}-\sqrt{624}=\sqrt{625}-\sqrt{9}=25-3=22[/tex]
Explicație pas cu pas:
Aplificare fiecare fractie cu conjugata numitorului....
