Direction of variation of a sequence
Definition :
A sequence
is increasing if for all
.
A sequence
is decreasing if for all
.
A sequence
is constant if for all
.
Example :
Study the direction of variation of the sequence u defined on by
=4n+3
The answer:
for all we have
. Then the sequence
is increasing
Proposition
Let f be a function defined on the interval and, for any natural number n,
=
.
If the function f is increasing on
, then the sequence u is increasing.
If the function f is decreasing on the interval
, then the sequence u is decreasing.