Show your work. 1. Use mathematical induction to establish that for every positive integer : [c4n+ 11dn-5) = 3+1 2. Use mathematical induction to establish that 7"-2" is divisible by 5 for every positive integer n. 3. Consider the sequence (S) - for which so = S = 1 and for every integer n 2: Sn = S-1 + 25.- (a) Calculate the value of $6. (b) Prove that all terms of the sequence ( S o are odd. 4. Consider the sequence (n o for which to = 2 and t = 1 and for every integer n 2: (a) Calculate the values of t. (b) Give an explicit formula fort