My son brought me a math problem to solve but I couldn't. Can anyone provide
a solution.
Given p, q, r, show series p/q, (p+rq)/(p+q), ((p+rq)+r(p+q))/((p+rq)+(p+q)), e.g., for the (n+1)th term, the numerator is the sum of the nth term's numerator plus r times the nth term's denominator, and the (n+1)th term's denominator is the sum of the nth term's numerator and denominator. It approaches the
square root of r.
I tried p=q=1, and r=2,3,4,5. It works well.
How to prove it?