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 u1=8 which is divisible by 8. Inductive hypothesis uk is divisible by 8.
Induction: uk+1=8×32k+uk 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 ****]
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.
I'm not sure what the above posters are saying - but all you need to do is:
Base case u1=8 which is divisible by 8. Inductive hypothesis uk is divisible by 8.
Induction: uk+1=8×32k+uk 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?
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 un is divisible by 8:
Base, inductive hypothesis, show part (a) without being told to explicitly, then do what I said.
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?
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 un is divisible by 8:
Base, inductive hypothesis, show part (a) without being told to explicitly, then do what I said.
To be fair I did manipulate slightly by adding uk 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
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 5f(k) (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 f(k+1)−f(k).