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
