UNSW Comp (2 Viewers)

Makematics

Well-Known Member
Joined
Mar 26, 2013
Messages
1,829
Location
Sydney
Gender
Male
HSC
2013
HOLY SHIT WHAT IS THIS EPIPHANY OMFG

Nuuuuuuuuuuuuuuuu wow I should've just wrote k=n+1
bad luck! :( anyways what i really wanna know is how you can actually prove this. Realise, i was also trying an induction in the last 5 minutes but to no avail.
 

RealiseNothing

what is that?It is Cowpea
Joined
Jul 10, 2011
Messages
4,591
Location
Sydney
Gender
Male
HSC
2013
bad luck! :( anyways what i really wanna know is how you can actually prove this. Realise, i was also trying an induction in the last 5 minutes but to no avail.
My approach:

Prove that:



Where 'p' is not divisible by 3.
 

Makematics

Well-Known Member
Joined
Mar 26, 2013
Messages
1,829
Location
Sydney
Gender
Male
HSC
2013
My approach:

Prove that:



Where 'p' is not divisible by 3.
Yep yep same here. I tried messing around with stuff like letting x=3^n but yeah, that didnt work out... was running out of time so just wrote down what i had observed from the results from the first few cases.
 

sbhs2013

New Member
Joined
Dec 18, 2011
Messages
8
Gender
Male
HSC
2013
Yep yep same here. I tried messing around with stuff like letting x=3^n but yeah, that didnt work out... was running out of time so just wrote down what i had observed from the results from the first few cases.
Then factorise and equate, something along the lines of that. I had fricking n+1 the whole time and I kept stumbling with the "k=2 when n=2"
 

RealiseNothing

what is that?It is Cowpea
Joined
Jul 10, 2011
Messages
4,591
Location
Sydney
Gender
Male
HSC
2013
Realise how did you do Q5? :eek:
1) Prove that 'n' has to be a multiple of 2 (fairly straight forward and obvious as you need an even amount of terms so that all 1's and -1's cancel out).

2)Prove that 'n' can be a multiple of 4. This is done by considering 4 terms:



Now this will always sum to 0 if only one of the x's is -1, and the other 3 are 1. So it is possible for 'n' to be a multiple of 4 by applying this method to all groups of 4.

3) Prove that 'n' can't be a multiple of 2 that isn't a multiple of 4, i.e.

Well you know the first terms will sum to 0, so you prove the last 2 terms can never equal 0, etc.
 

Makematics

Well-Known Member
Joined
Mar 26, 2013
Messages
1,829
Location
Sydney
Gender
Male
HSC
2013
i havent learnt harder 3u so my first reaction to Q4 was like "oh shiet, i need harder 3U skillz to do this"
 

Makematics

Well-Known Member
Joined
Mar 26, 2013
Messages
1,829
Location
Sydney
Gender
Male
HSC
2013
1) Prove that 'n' has to be a multiple of 2 (fairly straight forward and obvious as you need an even amount of terms so that all 1's and -1's cancel out).

2)Prove that 'n' can be a multiple of 4. This is done by considering 4 terms:



Now this will always sum to 0 if only one of the x's is -1, and the other 3 are 1. So it is possible for 'n' to be a multiple of 4 by applying this method to all groups of 4.

3) Prove that 'n' can't be a multiple of 2 that isn't a multiple of 4, i.e.

Well you know the first terms will sum to 0, so you prove the last 2 terms can never equal 0, etc.
alright well i was messing around with cases and wrote something along those lines. someone who did it was saying something about factoring out terms and then summing them.
 

RealiseNothing

what is that?It is Cowpea
Joined
Jul 10, 2011
Messages
4,591
Location
Sydney
Gender
Male
HSC
2013
I just realised for question 6, I could have written down the general formula:



which would have given me extra credit marks :(
 

Users Who Are Viewing This Thread (Users: 0, Guests: 2)

Top