You see you add the sum of the sin of pi/2, pi/4, pi/8... But maple does not know what it is.
But I found that it seems to have a finite limit...
It seems to be converging to something like 2.481... which doesn't get any google results for the first few digits the way most well known mathematical limits would.
Just a reminder the sin(pi/2) = 1, the sin(pi/4)=sq(2)/2, and then:
So anyway when you add these all up it apparently has a finite sum but it doesn't seem anyone has mentioned this particular limit before.