**Theorem 1**

Let `a in RR` then `lim_(n to infty)a/n=0.`

We will also use the fact that the codomain of sine function is `[-1,1].`

`lim_(n to infty)a_n=lim_(n to infty)sin n/n=`

We cannot calculate `sin infty,` but we know that its value must be between `-1` and `1.` Therefore, using theorem 1 we get

`lim_(n to infty)sin n/n=0`

As we can see **the sequence is convergent and its limit is equal to 0**.

The image below shows first 100 terms of the sequence. We can see that the sequence is alternating, but the terms are slowly approaching `x`-axis i.e. the sequence converges to zero.

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**Further Reading**