You are Here: Home

# Proof by induction help Tweet

Maths and statistics discussion, revision, exam and homework help.

This thread is sponsored by:
Announcements Posted on
Important: please read these guidelines before posting about exams on The Student Room 28-04-2013
Sign in to Reply
1. Proof by induction help

Could anyone explain to me for part a) what they have done here (the highlight parts)

For part b) Would my working here get full marks?

so true for n = 1
assume true for n = k

As are true then the sum of them is also true, therefore f(k+1) is divisible by 5.

As true for n = 1 => true for n>= 1 neZ+
True for n=k then as shown true for n=k+1 by mathematical induction

Is this sufficient as they have done different working.

thanks
2. Re: Proof by induction help
b)

You have shown that 2f(k+1) is div by 5 but you should write a bit why this implies that f(k+1) is div by 5.

Also, your statement "f(k)... are true" doesn't make much sense since f(k) is an expression not an equation. Try to keep your induction proofs mathematically as well as grammaticaly valid.
3. Re: Proof by induction help
a)

Does this make sense to you and does it help with the first part?

Second part:

Last edited by notnek; 15-06-2012 at 05:15.
4. Re: Proof by induction help
(Original post by notnek)
a)

Does this make sense to you and does it help with the first part?

Second part:

I'm still lost on part a), I don't see the first part how it would be (k+1), I thought it would be (k+1)/2 *(k+1+2) + (1/2)^k .

Also, how do they get (-1+1/2)?
5. Re: Proof by induction help
(Original post by thorn0123)
I'm still lost on part a), I don't see the first part how it would be (k+1), I thought it would be (k+1)/2 *(k+1+2) + (1/2)^k .
Could you explain which specific (k+1) you are talking about and could you also say why you think it should be (k+1)/2 *(k+1+2) + (1/2)^k ?

I can help you if I understand your reasoning.

Also, how do they get (-1+1/2)?
They have factorised. The first term is (-1) times and the second term is (1/2) times so you can take out a factor of .

Again, if you're still confused, can you tell me the specific part which you're confused about?
6. Re: Proof by induction help
(Original post by notnek)
Could you explain which specific (k+1) you are talking about and could you also say why you think it should be (k+1)/2 *(k+1+2) + (1/2)^k ?

I can help you if I understand your reasoning.

They have factorised. The first term is (-1) times and the second term is (1/2) times so you can take out a factor of .

Again, if you're still confused, can you tell me the specific part which you're confused about?
Well for part a) I thought the series would be for n = k+1 :

and in the solution they are saying add (k+1) + (1/2)^k to each side, but I don't understand why.

I am also doing (k+1)/2 (k+2) because the is

Thank you again for helping
7. Re: Proof by induction help
(Original post by thorn0123)
Well for part a) I thought the series would be for n = k+1 :

and in the solution they are saying add (k+1) + (1/2)^k to each side, but I don't understand why.

I am also doing (k+1)/2 (k+2) because the is

Thank you again for helping
What you are doing is not necessary and makes the question more complicated. I'll try to explain again what the solution has done because this technique is used in most induction questions involving summations.

Here's a simpler example that might help you:

The 1st line -> 2nd line is equivalent to adding i.e. in my second post, to both sides. Can you see how a very similar thing has been done in your example?

Your textbook should be able to explain this better than I can.
Last edited by notnek; 15-06-2012 at 20:55.
Sign in to Reply
Share this discussion:
Article updates
Moderators

We have a brilliant team of more than 60 volunteers looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is moderated by:
Reputation gems:
The Reputation gems seen here indicate how well reputed the user is, red gem indicate negative reputation and green indicates a good rep.
Post rating score:
These scores show if a post has been positively or negatively rated by our members.