Question

As n approaches infinity this sequence of partial sums could either converge meaning that the terms eventually approach some finite limit or it could diverge to infinity meaning that the terms eventually grow without bound. which do you think is the case here and why?

Short answer

The sequence is convergent.

Step-by-step solution

Given information

We are given a sequence we are asked whether it is convergent or divergent.

Explanation

As the value of n increases the difference between two consecutive terms is decreasing for a very large n the difference between two consecutive terms is so small that we can neglect it After that we get the same value even for an increasing value of n Hence we say that the sequence is convergent. And here is the case of convergent.