Question

va rog frumos sa ma ajutati!​

Answer 1

$\sqrt{1 - \frac{1}{2} } \times \sqrt{1 - \frac{1}{3} } \times \sqrt{1 - \frac{1}{4} } \times ... \times \sqrt{1 - \frac{1}{201} } =$

$\sqrt{ \frac{2}{2} - \frac{1}{2} } \times \sqrt{ \frac{3}{3} - \frac{1}{3} } \times \sqrt{ \frac{4}{4} - \frac{1}{4} } \times ... \times \sqrt{ \frac{2019}{2019} - \frac{1}{2019} } =$

$\sqrt{ \frac{1}{2} } \times \sqrt{ \frac{2}{3} } \times \sqrt{ \frac{3}{4} } \times ... \times \sqrt{ \frac{2018}{2019} } =$

$\frac{ \sqrt{1} }{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{3} } \times \frac{\sqrt{3} }{ \sqrt{4} } \times ... \times \frac{ \sqrt{2018} }{ \sqrt{2019} } =$

$\frac{ \sqrt{1} }{1} \times \frac{1}{1} \times \frac{1}{1} \times ... \times \frac{1}{ \sqrt{2019} } = \frac{ \sqrt{1} }{ \sqrt{2019} } = \frac{1}{ \sqrt{2019} }$