.n= n(n-1)(n+1) for all n > 2. 12. Use induction to prove (1 : 2) +(2-3)+(3-4)...
Use the Principle of Mathematical Induction to prove that (2i+3) = n(n + 4) for all n > 1.
Prove using mathematical induction that 3" + 4" < 5" for all n > 2.
Prove by induction that 1 1 15 15 + 1 35 35 + ... + = n 2n + 1 for every n > 1 4n2
Use induction to prove that 0–0 4j3 = n4 + 2n3 + n2 where n > 0.
Use induction and Pascal's identity to prove that (7) = 2" where n > 0.
(5) Use induction to show that Ig(n) <n for all n > 1.
(2) Prove by induction that for all integers n > 2. Hint: 2n-1-2n2,
Use induction to prove that for m > 5, 5m > 25m?.
Problem 44) Prove: n!> 2" for n24. Problem 45) Prove by induction: For n>0·AT- i=1
(a) Use mathematical induction to prove that for all integers n > 6, 3" <n! Show all your work. (b) Let S be the subset of the set of ordered pairs of integers defined recursively by: Basis Step: (0,0) ES, Recursive Step: If (a, b) ES, then (a +2,5+3) ES and (a +3,+2) ES. Use structural induction to prove that 5 (a + b), whenever (a, b) E S. Show all your work.