Use Exercise 1  to find a formula for (Compare with Exercise 2.)Exercise 1Suppose that Δ...

Use Exercise 1  to find a formula for

(Compare with Exercise 2.)

Exercise 1

Suppose that Δan = bn Show that

This formula is analogous to the calculus formula where Dg = f (D is the derivative operator). In the calculus formula, sum is replaced by integral, and Δ is replaced by derivative.

Exercise 2

Using induction, verify that the equation is true for every positive integer n.