A resursive sequence
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
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