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

Use Exercise 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

By experimenting with small values of n, guess a formula for

the given sum.

then use induction to verify your formula.