1. (5 pts) PROVE by using Mathematical Induction that 1*2 + 2*3 + 3*4 + ... + n*(n+1) = [n*(n+1)*(n+2)]/3, n>=1. 2. (5 pts) PROVE by using Mathematical Induction that 1 1 1 --- + --- + --- + ... + ------------ 1*3 (2n-1) (2n+1) 1 n ------ 2n + 1 , n>=1. 3. (5 pts) PROVE by using Mathematical Induction that 71 - 1 is evenly divisible by 6, for n >= 1. 4. (5 pts) PROVE by using Mathematical Induction that 1(1!) + 2(2!) + ... + n(n!) = (n+1)! - 1, for n >= 1 5. (5 pts) PROVE using the formal definition of Big O that 3n3 + 5n2 + 2n +1 is O(n) Your proof should be modeled after a similar problem I worked in class 6. (5 pts) SOLVE the following recurrence formula: T(n)= 2+ 2T(n/2) T(2) = 2 7. (5 pts) PROVE using the formal definition of Big O that 2n = O(n!) Your proof should be modeled after the one I did in class where I proved n! is O(n"). ---OVER