There exists a real number
such that the sequence
be the sequence of real numbers defined by its first term
and the recurrence relation
We look for a number
such that the announced sequence
will be geometric.
is geometric if, and only if,
Such a computation enables us to decide whether the sequence
is convergent or not. Here the sequence
is a geometric sequence whose ratio is equal to
, thus it is convergent and its limit is 0. By Thm 7.1, we conclude that
is convergent and its limit is equal to 12.