Prove by induction the following formula: For n 1,222 +23 +24 + ... + 2 = =2n+1 2. a) What is the base value for n? b) What is the Inductive hypothesis? c) What do you need to prove in Induction Step? d) Construct the whole proof with the proof structure. Prove for all integers that are > 1: 1 1 1 X 2 + 3 + n + = nx(n+1) n+1 a) What is the base value for n? b) What is the Inductive hypothesis? c) What do you need to prove in Induction Step? d) Construct the whole proof with the proof structure. Let the sequence defined by: a = 1, a2 = 8, an = an1 +2an-2 for n 3 Prove that: an = 3 2n-1 for all n N +2(-1)" a) What is the Inductive hypothesis? b) What do you need to prove in Induction Step? c) Construct the whole proof with the proof structure.