A run of 0's in a binary string s of length at least 1 is a substring s' of s consisting only of 0's, such that each end of the substring is either adjacent to a 1 or is also the end of the whole string s. For example, the string 101100 has two runs of 0's, one of length 1 and one of length 2 and the string 000 has one run of 0's of length 3, namely the whole string itself. Let R(n) be the total number of runs of O's, taken over al binary strings of size n 1. This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. For license purposes, the author is the University of British Columbia 1. Give values for R(1) and R(2): R(2) 2. Provide a recurrence relation for R(n), n 2 1. 3. Justify why your recurrence is correct. 4. Solve your recurrence, to express R(n) as a function of n. A run of 0's in a binary string s of length at least 1 is a substring s' of s consisting only of 0's, such that each end of the substring is either adjacent to a 1 or is also the end of the whole string s. For example, the string 101100 has two runs of 0's, one of length 1 and one of length 2 and the string 000 has one run of 0's of length 3, namely the whole string itself. Let R(n) be the total number of runs of O's, taken over al binary strings of size n 1. This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. For license purposes, the author is the University of British Columbia 1. Give values for R(1) and R(2): R(2) 2. Provide a recurrence relation for R(n), n 2 1. 3. Justify why your recurrence is correct. 4. Solve your recurrence, to express R(n) as a function of n