let-a-n-k-2-n-cos-pi-2-k-prove-that-a-n-ks-decreasing-2-let-b-n-a-n-cos-pi-2-n-find-lim-n-a-n-b-n-

Question Number 30488 by abdo imad last updated on 22/Feb/18

l e t a_{n} = \prod_{k = 2}^{n} c o s (\frac{π}{2^{k}}) . p r o v e t h a t (a_{n}) k s d e c r e a s i n g .

2) l e t b_{n} = a_{n} c o s (\frac{π}{2^{n}}) f i n d {l i m}_{n \to \infty} (a_{n} - b_{n}) .