Determine whether the sequence converges or diverges.If it converges, find the limit.

$\{0,1,0,0,1,0,0,0,1, \ldots\}$

Whether the sequence converges or diverges and obtain the limit if the sequence converges.

The sequence diverges.

Given:

Consider the sequence as an={0,1,0,0,1,0,0,0,1,...} .

Definition used:

If an is a sequence and limn→∞an exists, then the sequence an is said to be converges; otherwise it diverges.

Conclusion:

Here, the sequence formed by using only two values 0 and 1.

Also, the sequence an does not converge to neither 0 nor 1 or any other number.

Since limn→∞an does not exist and by using the definition of the sequence, it can be concluded that the sequence diverges.

Therefore, the sequence diverges.