Suppose that x(1)=1 and x(n+1)= 1 + 1/x(n), n=1,2,... Prove that the sequence {x(n)}, (n goes from 1 to infinity) converges and find its limit

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- Sep 22nd 2008, 08:56 PMSnooks02Limits of Sequences
Suppose that x(1)=1 and x(n+1)= 1 + 1/x(n), n=1,2,... Prove that the sequence {x(n)}, (n goes from 1 to infinity) converges and find its limit

- Sep 23rd 2008, 05:47 AMandrewlimits of sequences
Take this as an iterative process 1.e for n = 1 you get x(2) = 1+1/1 = 2, n = 2

X(3) = 1+1/2 = 1.5 .. . . .. and so on… if maintain the number of decimal places for example 2 decimal places, time comes when the subsequent values you get don’t change…. So your sequence will have converged…