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March 29, 2024, 06:31:47 am

Author Topic: 3U Maths Question Thread  (Read 1230361 times)  Share 

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RuiAce

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Re: 3U Maths Question Thread
« Reply #150 on: May 20, 2016, 11:18:12 pm »
+1
I remember the first time I tried this proof in my HSC I tried to do it with the full factorial expansions of each term, ever try it that way? I mean, not that you ever would, my teacher quickly steered me right  ;D
Well...


You'd end up having to prove THAT ugly thing somehow, oh dear

Not too sure if symmetry in the sum is required to get there without reverting steps and reintroducing the binomial coefficient but LOL not attempting that.
« Last Edit: May 20, 2016, 11:20:54 pm by RuiAce »

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #151 on: May 21, 2016, 12:47:58 am »
+1
Well...


You'd end up having to prove THAT ugly thing somehow, oh dear

Not too sure if symmetry in the sum is required to get there without reverting steps and reintroducing the binomial coefficient but LOL not attempting that.

Ahaha I think I got roughly to your third line before getting help back in 2014, definitely looks as disgusting as I remember it. If you are at UNSW and do Math 1131/41 next semester, you'll do stuff on series (mostly convergence tests though), so who knows, it might actually be doable  :P

RuiAce

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Re: 3U Maths Question Thread
« Reply #152 on: May 21, 2016, 08:50:38 am »
+1
Ahaha I think I got roughly to your third line before getting help back in 2014, definitely looks as disgusting as I remember it. If you are at UNSW and do Math 1131/41 next semester, you'll do stuff on series (mostly convergence tests though), so who knows, it might actually be doable  :P
*51, taking maths with actuarial :P

Too bad it's not an infinite sum or it would've been tempting to play around with a Taylor approximation. Finite sums are so different to limiting sums.

jakesilove

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Re: 3U Maths Question Thread
« Reply #153 on: May 21, 2016, 10:12:58 am »
+1
*51, taking maths with actuarial :P

Too bad it's not an infinite sum or it would've been tempting to play around with a Taylor approximation. Finite sums are so different to limiting sums.

I didn't realise you were at UNSW!
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jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #154 on: May 21, 2016, 11:56:48 am »
+1
*51, taking maths with actuarial :P

Too bad it's not an infinite sum or it would've been tempting to play around with a Taylor approximation. Finite sums are so different to limiting sums.

Ah that's right I forgot they separated you guys

RuiAce

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Re: 3U Maths Question Thread
« Reply #155 on: May 21, 2016, 01:46:30 pm »
+1
I didn't realise you were at UNSW!

Aha check signature :P

Ah that's right I forgot they separated you guys

I miss the days when maths used to be my easiest subject.

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #156 on: May 21, 2016, 08:55:41 pm »
+2

Aha check signature :P

I miss the days when maths used to be my easiest subject.

Welcome to the dark side!

amandali

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Re: 3U Maths Question Thread
« Reply #157 on: May 22, 2016, 02:03:03 pm »
0


i cant do part a) and part b (iii)

for part b (i) i got [ (1+x)^(n+1)-1 ]  /  n

jakesilove

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Re: 3U Maths Question Thread
« Reply #158 on: May 22, 2016, 02:21:54 pm »
+1
(Image removed from quote.)

i cant do part a) and part b (iii)

for part b (i) i got [ (1+x)^(n+1)-1 ]  /  n

Hey! This is a standard trick that you will learn to utilise as you continue doing these types of questions. Always just look for something that looks like it has been differentiated or integrated, and have a crack!



Jake
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RuiAce

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Re: 3U Maths Question Thread
« Reply #159 on: May 22, 2016, 02:32:07 pm »
+1
(Image removed from quote.)

i cant do part a) and part b (iii)

for part b (i) i got [ (1+x)^(n+1)-1 ]  /  n



Think about why that is true.




« Last Edit: May 27, 2016, 10:55:31 pm by jamonwindeyer »

katherine123

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Re: 3U Maths Question Thread
« Reply #160 on: May 24, 2016, 10:24:03 pm »
0
for part a) i got  prob(win1st or 2nd turn)= p+rq  and im not sure how to progress from there

RuiAce

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Re: 3U Maths Question Thread
« Reply #161 on: May 25, 2016, 09:31:56 am »
+2
for part a) i got  prob(win1st or 2nd turn)= p+rq  and im not sure how to progress from there





jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #162 on: May 25, 2016, 09:33:48 am »
+1
for part a) i got  prob(win1st or 2nd turn)= p+rq  and im not sure how to progress from there

Hey Katherine! I actually sat this HSC Paper, this is the last question, it was a bit of a doozy  ;)

Okay, so you are at this stage:



Great! Now, with these sorts of questions it is useful to keep an eye on where we are going. The required form has no 'q', so let's get rid of it. How? Well, we know the sum of all possible outcomes must be 1, therefore:



Have a go at the next question yourself, or check the solution below if you get stuck! It is a tricky question:

Spoiler
Okay, so the fact that we are considering the probability that A eventually wins the game, suggests that we are going to need some sort of infinite sum. Now, in the paper this actually annoyed me, because Part A totally throws you off track about how to start Part B, only coming back in near the end of the problem. Tricky! Let's reconsider the probability of winning after the first or second turn:



Now the third turn, then the fourth turn:


What we have set up is a pair of geometric sequences, which we can manipulate using infinite sum formulae to get the answer. Note that we can use this formula because, in both cases, the common ratio is less than 1  ;D





jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #163 on: May 25, 2016, 09:35:20 am »
+1





Simultaneous solutions it seems  ;D Virtually identical for you Katherine so either or  ;D

RuiAce

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Re: 3U Maths Question Thread
« Reply #164 on: May 25, 2016, 06:44:02 pm »
+1
Simultaneous solutions it seems  ;D Virtually identical for you Katherine so either or  ;D

You know I sat your MX1 paper right :P