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