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.]
In this problem we need to derive the formula for .
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