Use the technique given in Exercise 35. together with the result of Exercise 37b, to derive the formula for given in Table 2. [Hint: Take ak = k3 in the telescoping sum in Exercise 35.]

Solution:Step 1</p>

In this problem we need to derive the formula for .

Step 2</p>

Using the technique of telescoping which says that the sum of the sequence

where are the terms of the sequence.

To derive the formula for , we consider in the technique of telescoping and find the sum .

Using telescoping to find the sum of , we get

We know that . Using expansion of in the above sum, we get