Lecture 5

Learning objectives

After this class, you should be able to:

1. Write down the terms of multiple sums.
2. Determine a closed form expression for a multiple sum, using standard manipulations.
3. Given the first few terms of a series, consult the online reference to determine sequences that start with those terms.
4. Prove the correctness of closed form expressions for sums, using induction.

Reading assignment

1. Sec 2.4, Sec 2.5 - methods 0, 1, and 4 (only bounds for method 4).
2. Online encyclopedia of integer sequences: https://oeis.org
3. Review perturbation and repertoire techniques.

Exercises and review questions

• Questions on current lecture's material
  1. Exercise 2.14.
  2. Determine the series number for a sequence on the online reference, which starts with the following terms: 1, 4, 8, 16.
  3. Determine good bounds on the following sum using integration: sum k2-k, 1 ≤ k ≤ n.

• Questions on next lecture's material
  1. None.