What I notice about this sequence is that it converges to 4. It is infinitely increasing and is bounded from 3 ≤ y(n) < 4. It is not a Cauchy sequence because it does not oscillate even though with each iteration, the values get closer and closer together.
Below is a graph of the iterations of y(n). what can be observed by this graph is that y(n) gets closer and closer to 4 with each iteration. The line is very smooth and there are no kinks or waves. The sequence increases quite quickly as it approaches 4 with the first 20 or so iterations, then the increase of y(n) gets slower.
Below is an array of the iterations of y(n).
Below is the code that I wrote for finding the values of y(n)
