Question

please solve my question
I will make you brainlist
please help​

Answer 1

Answer:

Good question bro............

Answer 2

$\sqrt{(1 - \frac{1}{3})(1 - \frac{1}{4} )(1 - \frac{1}{5} )...(1 - \frac{1}{16}) } \\ \\ let \: \: \: z = (1 - \frac{1}{3} )(1 - \frac{1}{4} )(1 - \frac{1}{5} )...(1 - \frac{1}{16} ) \\ \\ take \: \: log_{2} \: \: on \: \: both \: \: sides \\ \\ log_{2}(z) = log_{2}((1 - \frac{1}{3})(1 - \frac{1}{4} )(1 - \frac{1}{5} )...(1 - \frac{1}{16)} ) \\ \\ log_{2}(z) = log_{2}( \frac{2}{3} ) + log_{2}( \frac{3}{4} ) + log_{2}( \frac{4}{5} ) + ... + log_{2}( \frac{15}{16} ) \\ becoz \: \: log(mn) = log(m) + log(n) \\ \\ log_{2}(z) = log_{2}(2) + log_{2}(3) + log_{2}(4) + ... + log_{2}(15) \\ - ( log_{2}(3) + log_{2}(4) + log_{2}(5) + ... + log_{2}(16) ) \\ \\ becoz \: \: \: log( \frac{m}{n} ) = log(m) - log(n) \\ \\ log_{2}(z) = log_{2}(2) - log_{2}(16) \\ \\ log_{2}(z) = log_{2}( \frac{2}{16} ) \\ \\ log_{2}(z) = log_{2}(2 {}^{ - 3} ) \\ \\ log_{2}(z) = - 3 log_{2}(2) \\ \\ log_{2}(z) = - 3 \\ \\ z = 2 {}^{ - 3} \\ \\ \\ now \: \: \: \sqrt[3]{z} = \sqrt[3]{2 {}^{ - 3} } = (2) {}^{ - \frac{ - 3}{3} } = 2 {}^{ - 1} = \frac{1}{2}$