The problem here is the sum,

.

We have no "nice" formula for working with .

However, in analysis we should learn how toapproximate.

Here is how we do it.*

Define the following function (see below).

Now the integral:

Is the area below this curve.

In this particular case it is:

And the area of the rectangles is (the width is 1):

Thus, we have:

In general we have,

.

Thus,

.

*)The credit goes to the proof of the Integral Test for series.