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# Fp1 proof by induction

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1. Need help with 8b.
Im not sure if I have done it correctly or how it shows the sequence is a multiple of 8.
Cheers.
http://m.imgur.com/ay6JzQq,UI3O2WW
2. Naaah - you want your inductive hypothesis to be "u_k is divisible by 8".
3. (Original post by Super199)
Need help with 8b.
Im not sure if I have done it correctly or how it shows the sequence is a multiple of 8.
Cheers.
http://m.imgur.com/ay6JzQq,UI3O2WW
If you show some working, I can make more comments about working and where the problem seems to be.
EDIT: Ignore me, my bad.
4. (Original post by Super199)
Need help with 8b.
Im not sure if I have done it correctly or how it shows the sequence is a multiple of 8.
Cheers.
http://m.imgur.com/ay6JzQq,UI3O2WW
I'm not sure what the above posters are saying - but all you need to do is:

Base case which is divisible by 8.
Inductive hypothesis is divisible by 8.

Induction: both terms are divisible by 8, we're done.

[Boring paragraph that I detest and is nothing more than A-Level masturbatory rigorousness about "by the principle of mathematical induction, since p(1) is true and whatever ****]
5. (Original post by Zacken)
I'm not sure what the above posters are saying
Being a chump - didn't scroll down -_-
6. (Original post by joostan)
Being a chump - didn't scroll down -_-
I've done exactly this with the same user before... I was all "please show some working" and it was there right. Massive
I wasn't referencing your post.
7. (Original post by Zacken)
I'm not sure what the above posters are saying - but all you need to do is:

Base case which is divisible by 8.
Inductive hypothesis is divisible by 8.

Induction: both terms are divisible by 8, we're done.

[Boring paragraph that I detest and is nothing more than A-Level masturbatory rigorousness about "by the principle of mathematical induction, since p(1) is true and whatever ****]
Wait so you haven't actually done any manipulation. You've just said Uk is divisble by 8. Then just said Uk+1 is divisible by 8 since both terms are divisble by 8?
8. (Original post by Super199)
Wait so you haven't actually done any manipulation. You've just said Uk is divisble by 8. Then just said Uk+1 is divisible by 8 since both terms are divisble by 8?
Yep - it's a 1/2 mark question at best. Normally they wouldn't have given you the part (a) and you would have had to do that yourself for the induction.

So, normally they'd have been: prove is divisible by 8:

Base, inductive hypothesis, show part (a) without being told to explicitly, then do what I said.
9. (Original post by Super199)
Wait so you haven't actually done any manipulation. You've just said Uk is divisble by 8. Then just said Uk+1 is divisible by 8 since both terms are divisble by 8?
Well yes. What else do you think is meant to be done?

What manipulation do you speak of?
10. (Original post by Zacken)
Yep - it's a 1/2 mark question at best. Normally they wouldn't have given you the part (a) and you would have had to do that yourself for the induction.

So, normally they'd have been: prove is divisible by 8:

Base, inductive hypothesis, show part (a) without being told to explicitly, then do what I said.
(Original post by Kvothe the arcane)
Well yes. What else do you think is meant to be done?

What manipulation do you speak of?
11. (Original post by Super199)
To be fair I did manipulate slightly by adding to both sides.
12. (Original post by Zacken)
To be fair I did manipulate slightly by adding to both sides.
Easy tiger. Right Ive got another one. Is this similar to previously?
11b. Also is there a reason to why they do f(k+1)-5f(k)? Why 5 in particular. I havent done induction in a while :/
http://m.imgur.com/cUxW0QK
13. (Original post by Super199)
Easy tiger. Right Ive got another one. Is this similar to previously?
11b. Also is there a reason to why they do f(k+1)-5f(k)? Why 5 in particular. I havent done induction in a while :/
http://m.imgur.com/cUxW0QK
It makes your life easier if they use (but if you weren't told to use 5f(k), I'd stick with using f(k)), it's the same principle yes. In general, for any inductive divisibility proof, consider .

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