Math Is Fun Forum

hannahr

Guest

induction

Hi, need help with this induction proof.

I cant seem to show the base case holds, maybe this is a silly mistake on my part or a typo in the book??

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: induction

Hi hannahr;

Base case is n = 0 and it is true.

Supposing it is true when n = k:

Then for  k + 1:

then:

Do the algebra:

We proved if k is true then k + 1 is true. We are done.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

hannahr

Guest

Re: induction

Oh wow thanks so much, completely forgot about trying n=0, silly me!!!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: induction

Hi hannahr;

Glad to help. Welcome to the forum!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

hannahr

Guest

Re: induction

Hi Bobbym, anothoer one I'm stuck on

Prove(by induction)
 

I have no idea how to do this one, some help would be greatly appreciated

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: induction

Hi hannahr;

That one is very different from the first. The first one is an elementary induction problem. This one is 100 levels past that. It is best proved using identities, not induction as far as I know.

This is a tentative proof.

For the first part of the inequality I would prove it like this:

Prove it true manually for 1,2,3, then,

Using the relationship:

Since:

We can now say:

Which implies:

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

hannahr

Guest

Re: induction

Hi again Bobbym, thanks for your reply, I dont fully understand what you have done but ill keep working at it. If i still don't get it i will ask you to go into a bit more detail

hannahr

Guest

Re: induction

Better yet I have an idea, you prove it using identitys, If you were to try and prove it by induction, wouldnt you assume the case

then try and prove it for N=n+1  i.e.

just an idea, do you see where I'm heading with this?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: induction

Hi hannahr;

I am not seeing how the n+1 step is making anything easier. That is the problem I am drawing a blank right there. Can you tell me where the problem comes from?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

hannahr

Guest

Re: induction

Well it comes from a book ''NUMBER THEORY An Introduction''  by Don Redmond. Its a question in the first problem set in the Induction section. So I assume you are required to prove by induction. I am also receiving help from another source so I'll post a solution if they can solve it hehe

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: induction

Page number please. Never mind I found it. I remember this book and I also remember why I disliked it so much!

Took a look at how the physicists do it and got so confused now I cant prove  x < x + 1.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: induction

This is kind of annoying since you can't prove a base case until n=5, but the induction proof is pretty simple.  Assuming

we want to prove that

You can see that the inequalities of the terms outside of the brackets are already known to be true, so if we can show that the terms inside of the brackets follow the same inequalities then our induction is complete.

which is true for all n>=0.

Last edited by TheDude (2010-08-20 01:51:45)

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Wrap it in bacon