Question

how do you prove this proposition using mathematical weak induction? 9n+14 <= 23n^2 please show your...

how do you prove this proposition using mathematical weak induction? 9n+14 <= 23n^2

please show your work and explain it.

Engineering   Computer-Science   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

We have the hypothesis :

Base Case :

For k = 1, we have

LHS

RHS

Thus, LHS <= RHS.

Thus, our hypothesis holds true for base case, k = 1.

Assumed Case :

We assume that out hypothesis holds true for k + 1.

That is,

Inductive Case :

For k + 1, we have

LHS

From our assumed case, we continue as

Also, since k is a positive integer, we further continue as

Thus, LHS <= RHS

Hence, proved via weak-induction.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove, using mathematical induction, that (1 + 1/ 2)^ n ≥ 1 + n /2 ,whenever...
Prove, using mathematical induction, that (1 + 1/ 2)^ n ≥ 1 + n /2 ,whenever n is a positive integer.
Prove by mathematical induction that for all odd n ∈ N we have 8|(n2 − 1)....
Prove by mathematical induction that for all odd n ∈ N we have 8|(n2 − 1). To receive credit for this problem, you must show all of your work with correct notation and language, write complete sentences, explain your reasoning, and do not leave out any details. Further hints: write n=2s+1 and write your problem statement in terms of P(s).
Please note n's are superscripted. (a) Use mathematical induction to prove that 2n+1 + 3n+1 ≤...
Please note n's are superscripted. (a) Use mathematical induction to prove that 2n+1 + 3n+1 ≤ 2 · 4n for all integers n ≥ 3. (b) Let f(n) = 2n+1 + 3n+1 and g(n) = 4n. Using the inequality from part (a) prove that f(n) = O(g(n)). You need to give a rigorous proof derived directly from the definition of O-notation, without using any theorems from class. (First, give a complete statement of the definition. Next, show how f(n) =...
Prove the following statement by mathematical induction. You will not receive any credit unless you give...
Prove the following statement by mathematical induction. You will not receive any credit unless you give a proof by induction. Foreverypositiveintegern?Z+, wehave1+2+...+n=n(n+1)/2
Consider the following expression: 7^n-6*n-1 Using induction, prove the expression is divisible by 36. I understand...
Consider the following expression: 7^n-6*n-1 Using induction, prove the expression is divisible by 36. I understand the process of mathematical induction, however I do not understand how the solution showed the result for P_n+1 is divisible by 36? How can we be sure something is divisible by 36? Please explain in great detail.
can you please show all the steps thank you... Prove by induction that 3n < 2n  for...
can you please show all the steps thank you... Prove by induction that 3n < 2n  for all n ≥ ______. (You should figure out what number goes in the blank.) I know that the answer is n>= 4, nut I need to write the steps for induction
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...
How do you show charging by induction using a comb, or another plastic item, and water?...
How do you show charging by induction using a comb, or another plastic item, and water? What materials are semiconductors? Describe two of these materials and their applications.
Conjecture a formula for the sum 1/1*3 + 1/3*5 + ... + 1/(2n-1)(2n+1), and prove your...
Conjecture a formula for the sum 1/1*3 + 1/3*5 + ... + 1/(2n-1)(2n+1), and prove your conjecture by using Mathematical Induction. PLEASE SHOW ALL WORK! PARTICULARLY WITH DEVELOPING FORUMLA!
Use the Principle of Mathematical Induction to show that the given statement is true for all...
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 1 + 4 + 4^2 + ... + 4^n - 1 = 1/3 (4^n - 1) Also, I looked at the process to get the answer in the textbook and when it comes to the step of k + 1, how does one just multiply by 3? Is there a property that I'm forgetting? Thank you!
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT