Question

Va rog frumos punctul b!!! Dau coroana!!

Answer 1

$\frac{ \sqrt{2} - \sqrt{3} }{\sqrt{6} } + \frac{ \sqrt{3} - \sqrt{4} }{ \sqrt{12} } + \frac{ \sqrt{4} - \sqrt{5} }{ \sqrt{20} } + \frac{ \sqrt{5} - \sqrt{6} }{ \sqrt{30} } + \frac{ \sqrt{6} - \sqrt{7} }{ \sqrt{42} } + \frac{ \sqrt{7} - \sqrt{8} }{ \sqrt{56} } \\ = \frac{ \sqrt{2} }{ \sqrt{6} } - \frac{ \sqrt{3} }{ \sqrt{6} } + \frac{ \sqrt{3} }{ \sqrt{12} } - \frac{ \sqrt{4} }{ \sqrt{12} } + \frac{ \sqrt{4} }{ \sqrt{20} } - \frac{ \sqrt{5} }{ \sqrt{20} } + \frac{ \sqrt{5} }{ \sqrt{30} } - \frac{ \sqrt{6} }{ \sqrt{30} } + \frac{ \sqrt{6} }{ \sqrt{42} } - \frac{ \sqrt{7} }{ \sqrt{42} } + \frac{ \sqrt{7} }{ \sqrt{56} } - \frac{ \sqrt{8} }{ \sqrt{56} } \\ = \frac{ \sqrt{2} }{ \sqrt{2} \times \sqrt{3} } - \frac{ \sqrt{3} }{ \sqrt{2} \times \sqrt{3} } + \frac{ \sqrt{3} }{ \sqrt{3} \times \sqrt{4} } - \frac{ \sqrt{4} }{ \sqrt{3} \times \sqrt{4} } + \frac{ \sqrt{4} }{ \sqrt{4} \times \sqrt{5} } - \frac{ \sqrt{5} }{ \sqrt{4} \times \sqrt{5} } + \frac{ \sqrt{5} }{ \sqrt{5} \times \sqrt{6} } - \frac{ \sqrt{6} }{ \sqrt{5} \times \sqrt{6} } + \frac{ \sqrt{6} }{ \sqrt{6} \times \sqrt{7} } - \frac{ \sqrt{7} }{ \sqrt{6} \times \sqrt{7} } + \frac{ \sqrt{7} }{ \sqrt{7} \times \sqrt{8} } - \frac{ \sqrt{8} }{ \sqrt{7} \times \sqrt{8} } \\ = \frac{1}{ \sqrt{3} } - \frac{1}{ \sqrt{2} } + \frac{1}{ \sqrt{4} } - \frac{1}{ \sqrt{3} } + \frac{1}{ \sqrt{5} } - \frac{1}{ \sqrt{4} } + \frac{1}{ \sqrt{6} } - \frac{1}{ \sqrt{5} } + \frac{1}{ \sqrt{7} } - \frac{1}{ \sqrt{6} } + \frac{1}{ \sqrt{8} } - \frac{1}{ \sqrt{7} } \\ = -\frac{1}{ \sqrt{2} } + \frac{1}{ \sqrt{8} } \\ = -\frac{1}{ \sqrt{2} } + \frac{1}{2 \sqrt{2} } \\ = -\frac{ \sqrt{2} }{2} + \frac{2 \sqrt{2} }{8} = -\frac{4 \sqrt{2} }{8} + \frac{ 2\sqrt{2} }{8} = -\frac{2 \sqrt{2} }{8} = -\frac{\sqrt{2} }{4}$