2) Prove that 1 + 3n < 4n for all n > 1. /5 Marks/
Prove that is an integer for all n > 0.
2. (D5) Let n = o(a) and assume that a =bk. Prove that <a >=<b> if and only if n and k are relatively prime.
Problem 5.1.3. Prove by induction on n that (1+ n < n for every integer n > 3.
(2) Prove by induction that for all integers n > 2. Hint: 2n-1-2n2,
| Prove that for n e N, n > 0, we have 1 x 1!+ 2 x 2!+... tnx n! = (n + 1)! - 1.
Say that a < 0) and k is a positive integer. Find a constant c such that tk edt < ceżat for all t > 0.
Prove using mathematical induction that 3" + 4" < 5" for all n > 2.
Problem 44) Prove: n!> 2" for n24. Problem 45) Prove by induction: For n>0·AT- i=1
Problem 7: Prove that for all integers n > 2, n+1 n 10-11 - n n +