CSCI 2405
Discrete Mathematics II
Fall 2017
Homework Assignment 4

Due: Friday, October 13, at the beginning of class.

Show your work for each problem. Don't guess. You should be able to convince a skeptical person that your answer is correct.

1. Give a formula for the sum for k = 1 to n of 3k+1, where n ≥ 1.

2. Give a formula for the sum for k = 1 to n of 5k+2, where n ≥ 1.

3. What is the value of the sum for k = 0 to 200 of 2(4^k)? Do not try to write it out as a number. Express it using powers of 4, such as 4²⁰⁰.

4. What is the sum for k = 0 to infinity of 3/(5^k)? Give the result as a number.

5. Using mathematical induction, prove that the sum from k = 1 to n of 1/(k(k+1)) is 1 - 1/(n+1) for all n ≥ 1.

6. Using mathematical induction, prove that The sum from k = 1 to n of k(k+1) is equal to (n(n+1)(n+2))/3 for all n ≥ 1.