(70 points) Consider the following binary tree Prefix codes from that tree were used to encode the following meassge 110100101011110101100011001110. Decode the message. 1. ( 80 points) Prove that for all natural numbers n1 121+231++n(n+1)1=n+1n. 2. (40 points) Give a recursive definition of the set S that contains all bitstrings that start with 1