Lecture 10

Learning objectives

After this class, you should be able to:

1. Define the following: the finite difference operator, rising factorial power, falling factorial power, indefinite sum, and definite sum.
2. Give the formula for the difference operator applied to xm.
3. Evaluate a sum using finite calculus, especially the sums of polynomials.

Reading assignment

1. Sec 2.6 - pages 47-51.
2. Page 52.

Exercises and review questions

• Questions on current lecture's material
  1. Determine a closed form expression for the sum of the cubes of the first n-1 positive integers, using finite calculus.
  2. Prove that (x+y)2 = x2 + 2x1y1 + y2.
  3. Exercise 2.7

• Questions on next lecture's material
  1. Give the expression for x-4.