Question

Cube root of (1-1/3)(1-1/4)....(1-1/16)

Answer 1

$= (1 - \frac{1}{3}) (1 - \frac{1}{4})(1 - \frac{1}{5})......(1 - \frac{1}{16})$

$= (\frac{2}{3}) (\frac{3}{4})( \frac{4}{5})......( \frac{15}{16})$

$= (\frac{2}{1}) (\frac{1}{1})( \frac{1}{1})......( \frac{1}{16})$

$= (\frac{2}{16})$

$= (\frac{1}{8})$

Cube root of (1/8) will be

$= {\frac{1}{8} }^{\frac{1}{3} }$

$= {\frac{1}{ {2}^{3} } }^{\frac{1}{3} }$

$= (\frac{1}{2})$

Answer is (1/2) { half }