**Given:**

Consider the sequence as
an=sinn
.

**Definition used:**

If
an
is a sequence and
limn→∞an
is exists, then the sequence
an
is said to be convergent otherwise it is divergent.

**Calculation:**

Obtain the limit of the sequence to investigate whether the sequence is converges or diverges.

Compute
limn→∞an=limn→∞sin(n)
. (1)

Use the subsequence
n=2mπ
in equation (1).

limn→∞sin(n)=limm→∞(sin(2mπ))=limm→∞(0)=0

Use the subsequence
n=(2m+12)π
in equation (1).

limn→∞sin(n)=limm→∞(sin((2m+12)π)) =limm→∞(1) =1

Here, it is observed that the term
an
oscillates between 0 and 1.

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

Therefore, the sequence is diverges.