The sequence is  .

If a sequence  is convergent, then there exist , where  is a constant.

.

Rewrite the sequence as shown below :

.

Substiute , note that as .

.

Note that the limit is of the form .

Apply LHospitals Rule :

So, LHospitals Rule tells us that if we have an indeterminate form or all we need to do is differentiate the numerator and differentiate the denominator and then take the limit.

Thus, the sequence converges to .

The sequence converges to .