par d,e,f and g show me all steps with good hand writing and thank ypu so much

Problem #2 (60 points) (a) Prove by mathematical induction that:n> Vn22 (b) Use mathematical induction to prove the following statement 1 +2+22+23 +.. +2n-2n+ for n20. (c) Prove that2+n(2n +1)/6 for the positive integer n. (d) Prove that 1.1!+2.2!.nn!-(n!-1 whenever n is a positive integer (e) Prove that 3+3.5+3.5+.+3.5"3S1)/4 whenever n is a nonnegative integer (1) Prove that for all integers n 1, s divisible by 3. (g) Prove that 21 divides 4 whenever n is a positive integer (h) Using induction, prove that for 2'-n2, 2 all integers n 20. (i) Prove by induction that the sum of the first n odd numbers is equal to n ,ie.(2 1-2