A resursive sequence

1. We define and for each we have Determine if the sequence converges or diverges.

[Sol]. We first try out some few terms. [We use as the iteration function.] We obtain the following:

We conjecture that this sequence converges and say it converges to then we are about to solve an equation like this: The solution are : . Since initial value the limit should be Next, we can use 'fixed method' to see if we have a solution for and graphically.

Indeed, we do see two intersections. We conclude that the sequence is convergent and its limit is

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