Compute N if:
N = 1 + 1/(2+1/(2+1/(2+...)))
P.S. This will probably be the last problem I will post for a long time, if again. Thank you all for all of your help. Without you, these problems would remain unsolved and I'd be in trouble.
Assume this converges (in fact we know it does but I wont go into that now,
Put:
X = 1/(2 + 1/(2 + 1/(2 + ...)))
Then:
X= 1/(2+X),
or:
X^2+2X - 1=0
or X = [-2 +/- sqrt(4+4)]/2 = +/-sqrt(2)-1
but as we know X>0, we have X=sqrt(2)-1, so
N = 1 + 1/(2 + 1/(2 + 1/(2 + ...))) = 1 + X = sqrt(2)
RonL