... advanced calculus... evaluate : K=Σ_(n∈N) (1/(2^(2n) (1+cos((π/2^n ))))) =?


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Question Number 121362 by mnjuly1970 last updated on 07/Nov/20

$. . . a d v a n c e d c a l c u l u s . . .$ $e v a l u a t e :$ $K = \sum_{n \in N} \frac{1}{2^{2 n} (1 + c o s (\frac{π}{2^{n}}))} = ?$
Commented by mindispower last updated on 07/Nov/20

$h a v e y o u t h e r e s u l t n o t t h e a n s w e r$
	Answered by mindispower last updated on 07/Nov/20

	$i w i l l t r y b u t n o t s u r, t t h i s \frac{1}{1 + c o s (\frac{π}{2^{n}})} s e e m s$ $b e e i m p r e s s i v, m a y b e e t u r n i t o n \frac{1}{2} (1 + {t g}^{2} (\frac{π}{2^{n + 1}}))$
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