Sequences and Summations

Please see the attached file for the fully formatted problems. Practice problem 20 List the first 10 terms of each of these sequences. a) The sequence whose nth term is the larges integer k such that b) The sequence whose nth term is c) The sequence whose nth term is ⌊ d) The sequence whose nth term is the ...continues

Matrices - Find the product AB for total of 3 pairs of matrices.

Find the product AB, where a) A = [] B = [] b) A = [] B = [] c) A = [] B = [] (Please see the attached file to view the questions)

Complexity of algorithms

How much time does an algorithm take to solve a problem of size n if this algorithm uses 2n^2 + 2^n bit operations, each requiring 10^-9 second, with these values of n? i) 10 ii) 20 iii) 50 iv) 100 I need help with a question, the attachment contains the question as well as what I think is the answer. Could someone ple ...continues

Prove by Mathematical Induction

Prove that 3^n < n! if n is an integer greater than 6.

Pigeonhole Principle

1. Explain how the pigeon-hole principle can be used to show that among any 11 integers, at least two must have the same last digit.

Representing Graphs and Graph Isomorphism

Represent the given graph using an adjacency matrix. Please see the attached file for the fully formatted problems.

There are 7 drawers in a tool box. There are 100 tools. What is the largest number of tools that must reside in the same drawer?

1. There are 7 drawers in a tool box. There are 100 tools. What is the largest number of tools that must reside in the same drawer?

Combinations

Could someone show me how to solve the following. 20.How many different license plates can be made if each license plate consists of three letters followed by three digits or four letters followed by two digits?

Recursive Algorithm

23. Give a recursive algorithm for computing n * a using only addition, where n is a positive integer and a is a real number. (add a to itself n times).

Binary to Decimal Conversion

The binary expansion of an integer is 101001. Show how you compute the equivalent decimal value.