please answer 2 and 6 only

Exercise 1.4 Prove the following statements. 1. Prove by induction on n> 1 that i1/2 = 1-1/2" 2. Prove by induction on n > 0 that _, 21 = 2n+1 - 1. 3. Prove ! (21 - 1) = np. 4. Prove that (n + 1)2 = O(na). 5. Prove 2 lg(n!) > n Ign, where n is a positive integer greater than 2. 6. The number generated by the formula na + n + 17 is prime for n > 0, where n is an integer. Either prove it or disprove it by counterexample