Problem 2. Let k > 2 be an integer, and let S be the set of all binary strings in which every block of zeroes has length less than k, and every block of ones has length at least k. Find an unambiguous expression for S, and use it to prove that the generating series for S weighted by length is given by (1 - x)(1 1 + xk) s(1) = 1 - 2.+ 22 xk+1 +22k (It may be helpful to consider a set U consisting of the allowable blocks of zeroes and a set V containing the allowable blocks of ones, and to compute u and y separately before s. ) Problem 2. Let k > 2 be an integer, and let S be the set of all binary strings in which every block of zeroes has length less than k, and every block of ones has length at least k. Find an unambiguous expression for S, and use it to prove that the generating series for S weighted by length is given by (1 - x)(1 1 + xk) s(1) = 1 - 2.+ 22 xk+1 +22k (It may be helpful to consider a set U consisting of the allowable blocks of zeroes and a set V containing the allowable blocks of ones, and to compute u and y separately before s. )