induction

  1. E

    Induction Proof of Sum of n positive numbers

    I am not sure if this is the right place, but it does appear in my calculus book. " Proove by induction that for all n real, positive numbers a1, a2, a3, ..., an that follow the rule a1a2a3...an = 1, the following expession is true: \sum_{i=1}^{n} a_{i} \geq n " I have tried working it out...
  2. R

    Demonstration by Induction

    Hi, I've been trying to demonstrate this(Worried): I know that $d_1=1, d_2=10, d_3=50, d_4=248$ and for $n \geq 5 ,d_n = 5d_{n-1} - 4d_{n-4} $. Demonstrate for all $n \in \mathbb{N} $ that: $$P(n): d_n < n \cdot 3^{n+1}. $$ I need to demostre this using the induction principle. My doubt is...
  3. B

    mathematical induction with an inequality

    Dear all, I am having some trouble with this question. I looked at the markscheme and it doesn't really make sense to me. Please would someone be able to explain it? Thank you,
  4. O

    False proof by induction

    There's this classic proof by induction that is FALSE: The claim is that cars are all the same colour. This is equivalent to the claim that any set of cars must contain cars of the same colour. The claim is trivially true for the base case of n = 1 cars since, after all, a car has only one...
  5. ACARROT

    More Inductive Proof Questions

    I want to have a little 'le cry'. Earlier today, I made a super detailed and tidy post on my question, but for some reason it didn't post(I think it was because of my internet), and now I've got to type it all again, and with less care and attention to detail. :( Anyways, not so long ago, I had...
  6. ACARROT

    Confusion in Inductive Proofs

    Hey guys, I've been lurking around this site for a while, but I decided to finally stick in a question. Well, two, but I'll post one first and see if I can figure out the next one with the advice or help I get. I will post the question and then my working out and then what I'm confused about...
  7. S

    Proof that A^n < N!

    For any positive integer A, there is an integer N, which of course can vary depending on A, so that for all n >= N, A^n < n!. How am I supposed to show this? Do I need to show A^n = Big-O of n! or use induction? I tried both and I can't seem to figure it out.
  8. M

    Elementary number theory proof problem

    Okj guys I'm sitting on this one forever and just can't do it. Questions: Show that [1] is equivalent to [2] with a logical proof and proof that [3] implies [2] and proof the statement [3], if it's true [1] Is T a not empty subset of the natural numbers N, that means their exists an X ∈ T, that...
  9. M

    strong maths induction proving

    Let a0, a1, a2, . . . be the sequence defined recursively asa0 = 1, a1 = 2, ak = ak−1 + ak−2 for each integer k ≥ 2. Use strong mathematical induction to prove that an ≤ 2nfor each integer n ≥ 0. This is what i have so far with my working.Let P(n) be the statement that an≤2n Basic step: Prove...
  10. D

    Proof By Induction and Direct Approach

    Hi all, I just started class and already have no clue what I'm doing. I've looked through my notes, looked through the lecture slides, and tried to google how to do it and watch YouTube videos but I still can't figure out how to do it.Let asubn =1/(n(n+1)) : Compute asub1; asub1 +asub2; asub1...
  11. M

    Mathematical Induction.

    1+4+7+...+(3n-2)=n(3n-1)/(2) Step 1: n=1 Show that it is true. Step 2: n=k step 3: n=k+1 step 4: proof I did this in the order provided in the picture below. Did I plug in everything right? is it simply just not having good algebra skills that is not getting me these the equation to be correct?
  12. E

    proof by induction

    prove by induction: (n+1)^n \geq (2^n)n! for all natural numbers n thanks for your help.
  13. Q

    Simple mathematical induction

    Okay, so I've just started with mathematical induction today, and I've encountered a problem which I cannot seem to solve (probably because I haven't done any math related work in a long time). It's just the simple problem of proving the following: n^2>=2n+1 (for: n>=3) I've worked it out as...
  14. D

    Mathematical Induction Proof w/ maximum of a function

    I am trying to write up this proof but don't know where to start. Let f : \{1,\cdots, n\} \rightarrow \mathbf N be a function. Then there is some q \in \{1, \cdots, n\} such that f(q)\ge f(i) for all i \in \{1, \cdots, n\}. Any assistance would be greatly appreciated.
  15. G

    Mathmatical Induction

    I am attempting to use the principles of mathematical induction to prove these 2 propositions true for all natural numbers n. I really need someone to hold my hand through these as I am completely lost. I can't even figure out how to type them in the website correctly so here is a picture of...
  16. B

    prove 17^200 - 1 is divisible by 10

    for 17^200 - 1 is divisible by 10, would I have to get 17^200 to like (17^40)^5 - 1 as n^5-1 and then go from there? what is the best way to proof this type of problem?
  17. B

    Prove n^2 > 10n + 126 for all n > n_0

    I have found n_0 or the first number that satisfies n^2 > 10n + 126 which is n_0 = 18 I guess i am getting lost in the inductive step where (K+1)^2 = 10(k+1) + 126. I just dont know where to go from here that shows that n>=n_0
  18. T

    Help with the formal proofs related to induction

    Hey everyone, I was wondering if someone can show me formal proofs to this exsercises. I got stuck and I really don't know how to write a formal proof of this. So if someone can help with this I'd be greatful! Thanks :)
  19. L

    Strong Induction with closed-form expression

    I have to use strong induction to solve a closed-form expression. I haven't found an example that can explain it to me... https://docs.google.com/document/d/1zBnN_yexeWEFgO3pWldEuB91izlflTA_5iigxmn8lyo/edit?usp=sharing I think I have to make n=1 first. I got 1/4 (I don't know if I'm...
  20. B

    Proof by Mathematical Induction

    This is a challenge problem that my instructor gave, I have never been taught how to do induction proofs before. I don't want the answer but just some tips on how to get started or What I could do first. We just started the chapter on derivatives so I am unsure of all the rules that I can apply...