5. Prove that U(2") (n > 3) is not cyclic.
Prove that is an integer for all n > 0.
Use the Principle of Mathematical Induction to prove that (2i+3) = n(n + 4) for all n > 1.
Prove by mathematical induction (discrete mathematics)
n? - 2*n-1 > 0 n> 3
Problem 7: Prove that for all integers n > 2, n+1 n 10-11 - n n +
2) Prove that 1 + 3n < 4n for all n > 1. /5 Marks/
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.
.n= n(n-1)(n+1) for all n > 2. 12. Use induction to prove (1 : 2) +(2-3)+(3-4) +...+(n-1).n [9 points) 3
| Prove that for n e N, n > 0, we have 1 x 1!+ 2 x 2!+... tnx n! = (n + 1)! - 1.