Question 6: A block in a bitstring is a maximal consecutive substring of 1's. For example, the bitstring 1100011110100111 has four blocks: 1, , and 111 For a given integer n1, consider all 2" bitstrings of length . Let Bn be the total number of blocks in all these bitstrings For example, the left part of the table below contains all 8 bitstrings of length 3. Each entry in the rightmost column shows the number of blocks in the corresponding bitstring Thus 0 1012 .Determine Bi and B .Let n 3 be an integer - Consider all bitstrings of length nthat start with 0. What is the total number of blocks in these bitstrings? - Determine the number of blocks in the bitstring - Determine the mber of blocks in the bitstring - Let k be an integer with 2 Sk 1. Consider all bitstrings of length n that start with ke-1 Prove that the total number of blocks in these bitstrings is equal to 2-B- -Prove that - Use 1 2+2+2+2"-21, to prove that * Prove that (1) also holds for n = 2. .Let n2 3. Prove that Bn 2-2+2 B-1 Hint: Write (1) on one line. Below this line, write (1) with replaced by n-1. . Prove that for every n 21, 2n