Evaluate this infinite product (Posted on 2008-06-05)

	Submitted by pcbouhid
Rating: 5.0000 (1 votes)
Solution:	(Hide)
Using the hint given, and the equality cos(2a) = 2*cos2(a) - 1, we arrive at the product: P = cos(pi/4) * cos(pi/8) * cos(pi/16) * ... To evaluate this, we use cos(a) = sin(2a)/2sin(a). The product of the first n terms of P simplify to: Pn = sin(pi/2) / [2n * sin(pi/2n+1)]. The limit of Pn as n tends to infinity, after making 2n+1 = pi/x, leads us to P = 2/pi.

	Subject	Author	Date
	re: Analytical solution ======== what if?	pcbouhid	2008-06-08 02:11:44
	Analytical solution	Daniel	2008-06-07 15:40:35
	re: Identity of numeric value ------ a first hint	pcbouhid	2008-06-06 20:03:37
	Identity of numeric value	Paul	2008-06-06 16:03:28
	For what it's worth (numerical value)	Charlie	2008-06-05 12:27:29