Previous in Relation and Functions Next in Relation and Functions
Question Number 30488 by abdo imad last updated on 22/Feb/18
$${let}\:\:\:{a}_{{n}} =\:\prod_{{k}=\mathrm{2}} ^{{n}} \:{cos}\left(\frac{\pi}{\mathrm{2}^{{k}} }\right)\:.{prove}\:{that}\:\left({a}_{{n}} \right)\:{ks}\:{decreasing}. \\ $$$$\left.\mathrm{2}\right)\:{let}\:{b}_{{n}} ={a}_{{n}} {cos}\left(\frac{\pi}{\mathrm{2}^{{n}} }\right)\:\:{find}\:{lim}_{{n}\rightarrow\infty} \left({a}_{{n}} \:−{b}_{{n}} \right). \\ $$