Hope this will help.
Problem 3. Find the exact solutions to the following recurrences and prove your solutions using induction...
Use the Principle of Mathematical Induction to prove that (2i+3) = n(n + 4) for all n > 1.
2) (3 pts) Use mathematical induction to show that when n is an exact power of 2, the solution of the recurrence 2, ifn=2 T(n) =127G)+n, ifn=2.for k > 1 ISI(72) = n lg n.
Use mathematical induction to show that when n is an exact power of 2, the solution of the recurrence: { if n 2 2 T(n) for k> 1 if n 2 T(n) 2T(n/2) is T(n) n log
Problem 5.1.3. Prove by induction on n that (1+ n < n for every integer n > 3.
Problem 30. Prove that N, Z, Q and R are infinite sets. (HINT: Prove by induction on n that is f: NN then (3k N(Vj Nn)k> f(j). Then conclude that f cannot possibly be onto N. A similar strategy works for Z, gq and R as well.)
Please Prove. Prove 2 n > n2 by induction using a basis > 4: Basis: n 5 32> 25 Assume: Prove:
Prove by mathematical induction (discrete mathematics) n? - 2*n-1 > 0 n> 3
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 >
Use induction to prove that 0–0 4j3 = n4 + 2n3 + n2 where n > 0.