Question

Prove using induction that: a) 2n < n! , ∀n ≥ 4 (b) n! < nn...

Prove using induction that: a) 2n < n! , ∀n ≥ 4 (b) n! < nn ∀n > 0.

Homework Answers

Answer #1

Solution a)

Solution b)

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove the following using induction: (a) For all natural numbers n>2, 2n>2n+1 (b) For all positive...
Prove the following using induction: (a) For all natural numbers n>2, 2n>2n+1 (b) For all positive integersn, 1^3+3^3+5^3+···+(2^n−1)^3=n^2(2n^2−1) (c) For all positive natural numbers n,5/4·8^n+3^(3n−1) is divisible by 19
Prove using mathematical induction that 20 + 21 + ... + 2n = 2n+1 - 1...
Prove using mathematical induction that 20 + 21 + ... + 2n = 2n+1 - 1 whenever n is a nonnegative integer.
Use Mathematical Induction to prove that 3 | (n^3 + 2n) for all integers n =...
Use Mathematical Induction to prove that 3 | (n^3 + 2n) for all integers n = 0, 1, 2, ....
Use mathematical induction to prove that for each integer n ≥ 4, 5n ≥ 2 2n+1...
Use mathematical induction to prove that for each integer n ≥ 4, 5n ≥ 2 2n+1 + 100.
(10) Use mathematical induction to prove that 7n – 2n  is divisible by 5 for all n...
(10) Use mathematical induction to prove that 7n – 2n  is divisible by 5 for all n >= 0.
Proof the following theorem using mathematical induction: 2n ≥ 3n, for n ≥ 4
Proof the following theorem using mathematical induction: 2n ≥ 3n, for n ≥ 4
Let Nn be the integer whose decimal expansion consists of n consecutive ones. Prove that (Nn,Nm)...
Let Nn be the integer whose decimal expansion consists of n consecutive ones. Prove that (Nn,Nm) = N(n,m). Example: N3= 111 N6=111111. please prove by induction and using a general case
Show all the steps... Prove by induction that 3n < 2n  for all n ≥ ______. (You...
Show all the steps... Prove by induction that 3n < 2n  for all n ≥ ______. (You should figure out what number goes in the blank.)
Prove the following statement by mathematical induction. For every integer n ≥ 0, 2n <(n +...
Prove the following statement by mathematical induction. For every integer n ≥ 0, 2n <(n + 2)! Proof (by mathematical induction): Let P(n) be the inequality 2n < (n + 2)!. We will show that P(n) is true for every integer n ≥ 0. Show that P(0) is true: Before simplifying, the left-hand side of P(0) is _______ and the right-hand side is ______ . The fact that the statement is true can be deduced from that fact that 20...
Consider the following statement: if n is an integer, then 3 divides n3 + 2n. (a)...
Consider the following statement: if n is an integer, then 3 divides n3 + 2n. (a) Prove the statement using cases. (b) Prove the statement for all n ≥ 0 using induction.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT