Use induction and Pascal's identity to prove that (7) = 2" where n > 0.
Use induction to prove that 0–0 4j3 = n4 + 2n3 + n2 where n > 0.
Prove by induction that 1 1 15 15 + 1 35 35 + ... + = n 2n + 1 for every n > 1 4n2
.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
8. Use mathematical induction to prove that n + + 7n 15 3 5 is an integer for all integers n > 0.
Problem 44) Prove: n!> 2" for n24. Problem 45) Prove by induction: For n>0·AT- i=1
Prove each problem, prove by induction
3) Statementn-1 5 25(2m-1) forn2 1 4 Statement Suppose: bo1 . b,-2b-1 + 1 for t 1 en fort >
8. Use mathematical induction to prove that F4? = FmFn+1 Yn> 1, where Fn is the n-th Fibonacci number. k=1
Prove using mathematical induction that 3" + 4" < 5" for all n > 2.
(5) Use induction to show that Ig(n) <n for all n > 1.