Rules for convergent sequences
Let
and
be
convergent sequences. Then the following statements hold.
- The sequence
is convergent, and
-

holds.
- The sequence
is convergent, and
-

holds.
- For
,
we have
-

- Suppose that
and
for all
.
Then
is also convergent, and
-

holds.
- Suppose that
and that
for all
.
Then
is also convergent, and
-

holds.