Re: Math & logic problems :-)
Reply #94 - October 09, 2010, 01:37 PM
No idea HO. Though here's a problem:
x1,x2,x3,...,xn for all n >= 3 satisfy the equations:
x1 = 1 + (1 / x2), x2 = 1 + (1 / x3),..., xn-1 = 1 + (1 / xn)
and also: xn = 1 + (1 / x1).
Show that:
i) x1,x2,x3,...,xn > 1
ii) x2 - x3 = -(x2 - x3) / (x2x3)
iii) x1 = x2 = x3 = ... = xn
Hence find the value of x1.
My solution to this works backwards, but I'm curious as to how you guys would approach this.