Let n be a positive integer. Give a recursive algorithm for computing the sum of the first n positive integers by filling in the boxes in the procedure below with the expressions n, n – 1 or 1. Note: You have to use some expressions more than once, but each box must contain only one of those expressions. - procedure sum( : positive integer) if then sum 1 n else sum + sum

Natasha and Rodrigo are in a class of 30 students that selects 4 leaders. How many ways are there to select the 4 leaders so that either Natasha and Rodrigo are both selected or Natasha and Rodrigo are both not selected?  Show all work.   You do not need to multiply out the final answer.

Consider the list of numbers: 2n-1, where n first equals 2, then 3, 4, 5,6,…What is the smallest value of n for which 2n -1 is not a prime number.  Show all your work.

The first question I have the answer. The second question is: explain how this compares with 20C5 and 20P5.