Exercise.
Let (
)
be a sequence of real numbers with the following property:
for every odd
+1=-
.
(For example,
=(-1)
is such a sequence.
So is the sequence
12,-12,13,-13,14,-14,15,-15,
.)
Suppose
as
. Use
>0
-
<
to show that
-
as
.
Deduce from the theorem on the uniqueness of limits that =0.