## 3.1. Sequences

### Examples 3.1.12:

This might seem difficult because trig functions such as *sin*
and *cos* are often tricky. However, using the Pinching
theorem the proof will be very easy.

We know that *| sin(x) | 1*
for all *x*. Therefore

for all-1 sin(n) 1

*n*. But then we also know that:

The sequences-1/n sin(n)/n 1/n

*{1/n}*and

*-1/n*both converge to zero so that the Pinching theorem applies and the term in the middle must also converge to zero.

To prove the statement involving the *cos* is similar and left
as an exercise.