Thread: How to solve this recursive equation/recurrence relation

How to solve this recursive equation ? The answer is also given. can anyone give an detailed explanation how to solve it ??????

q(t) = 4 − (2/q(t-1)), with t>=2 -----------(1)


Answer is :
q(t) = (2 - sqrt(2)) +[ (2.sqrt(2) / (1- (3-2.sqrt(2))^t] ------------------(2)


Now, equation (1) is not a simple homogeneous linear second order equation which we normally use to solve recurrence problems. The product term q(t).q(t-1) makes the polynomial equation of higher order. Can anyone kindly explain me in detail the solution procedure of the equation ???? It will be very helpful if you write your detailed solution procedure in a piece of paper and send me that as a scanned copy or PDF.

See attachment.

Hey avhi000.

This is not an answer to your question, but have you studied continued fractions? This looks like a continued fraction and if the form is recognized then the appropriate result could be used.