Consider the convergent sequence with terms defined by
Let . Find the value of
and the value of
such that
for all
for each of the following values of
:
-
,
-
,
-
,
-
,
-
.
First, we know
since , so by (10.10) on page 380 of Apostol we know the limit is 0.
Then we have,
We reversed the inequality sign in the final step since since
. Thus, if
then for every
we have
. We compute for the given values of
as follows:
-
implies
.
-
implies
.
-
implies
.
-
implies
.
-
implies
.