Explicație pas cu pas:
[tex]\frac{ \sqrt{1} - \sqrt{2}}{ \sqrt{1 \cdot 2} } = \frac{ \sqrt{1} - \sqrt{2}}{ \sqrt{1}\cdot \sqrt{2} } = \frac{1}{ \sqrt{2} } - \frac{1}{\sqrt{1}} \\ [/tex]
atunci:
[tex]a = \frac{\sqrt{1} - \sqrt{2}}{ \sqrt{1 \cdot 2}} + \frac{\sqrt{2} - \sqrt{3}}{\sqrt{2 \cdot 3}} + \frac{\sqrt{3} - \sqrt{4}}{\sqrt{3 \cdot 4}} + ... + \frac{\sqrt{98} - \sqrt{99}}{\sqrt{98 \cdot 99}} + \frac{\sqrt{99} - \sqrt{100}}{\sqrt{99 \cdot 100}} = \\ [/tex]
[tex] = \frac{1}{ \sqrt{2} } - \frac{1}{\sqrt{1}} + \frac{1}{ \sqrt{3} } - \frac{1}{\sqrt{2}} + \frac{1}{ \sqrt{4} } - \frac{1}{\sqrt{3}} + ... + \frac{1}{ \sqrt{99} } - \frac{1}{\sqrt{98}} + \frac{1}{ \sqrt{100} } - \frac{1}{\sqrt{99}} \\ [/tex]
[tex]= - \frac{1}{\sqrt{1}} + \frac{1}{ \sqrt{100} } = \frac{1}{10} - 1 = - \frac{9}{10} \\ [/tex]
