# How do you do this?

##### 1 Answer

See below:

#### Explanation:

The sequence is

Although it is rather clear from inspection that this sequence does not converge, a more formal proof can be given by several different approaches.

A more advanced approach would be to notice that the series has sub-sequences that converge to different limits (namely

A direct approach from the definition uses a proof by contradiction. We assume that a limit

Since

Similarly

Thus

Thus, we end up with