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Re: Discrete Maths Sem 2 2016 Thing with the Bezout lemma is that it's a one-way implication. The reverse way doesn't imply "equals", it implies "divides" (check the notes) So yeah I was thinking about the need to write the proof backwards to prove that they both divide each other, and hence...

Re: Discrete Maths Sem 2 2016 Whoops yeah meant that, thanks _____________________________ \text{Prove that }\gcd(a,b)=\gcd(a,a-b)

Re: Discrete Maths Sem 2 2016 \text{Assume that in the expansion of }(x+y+z)^{20}(x+y)^{15}\text{ all the like terms are collected.}\\ \text{How many distinct terms are there?} \text{So I analysed the question by considering the general algebraic term }x^\alpha y^\beta z^\gamma\\ \text{Which...

Yeah I've seen that question before as well. I'm reluctant to give into exhaustion but if it appears in the exam I'm gonna do it because I have no choice

Not convinced. Why?

\text{From my understanding of the integral test:}\\ \text{The convergence/divergence of }\int_{c}^\infty f(x)dx\text{ implies the convergence/divergence of }\sum_{k=c}^\infty a_k\\ \text{where }a_k=f(k) \forall k=c, c+1, \dots \text{Is the converse necessarily true? i.e. does the convergence...

Margaret Grove, whilst showing the formula, never uses it in any worked example Because it is a syllabus, it is prone to jumping heaps of steps so that the document isn't too large.

Yeah as InteGrand said, what necessary condition?

^Why is it that virtually all of them are from the past paper book lol But in regards to Q2, I also have that problem. \text{Q3: }A=\{0\}, B=\{1\}\\ \text{and }f(0)=2, f(1)=3\text{ will suffice.}

Fortunately first year first sem is the easiest to get a good enrolment with though.

Actually getting that ideal timetable pre-planned puts you one step ahead of everyone else because it'll save a lot of hassle later on. But don't forget that classes do have a maximum capacity. What might be your ideal timetable may be lost if you're a tad too slow with the enrolment procedures.

Re: UNSW chit chat thread 2016 Upcoming Tuesday

Re: Discrete Maths Sem 2 2016 How many strings of eight lowercase letters of the English alphabet contain: c) the letters x and y, with x occurring before y (anywhere before y), if all the letters are distinct? So I get the need to introduce 24P6. How would I finish it off from here?

Ah never mind. I don't have that paper with me right now, so I'm gonna apologise - I think I typed the question wrong this whole time.. Sent from my iPhone using Tapatalk

Re: Discrete Maths Sem 2 2016 x \sim y\text{ iff }\exists k \in \mathbb{Z}\text{ s.t. }x-y=2k\pi \text{Proven in a): }\sim\text{ is an equivalence relation}\\ \text{Found in b): }\mathbb{R}\text{, partitioned into a set of equivalence classes }[x]\\ \text{for }x\in \mathbb{R}\text{ is}\\...

Are you sure that it converges absolutely? Or were you not referring to my original question and instead the one Paradoxica used Further reference: I applied the limit form of the comparison test with 1/n

Well ok, I didn't want to use the word "trivial" because I figured there wouldn't be one. But otherwise I don't know what word would be appropriate to use

It's easier to deal with, but I was hoping for a more obvious method

Yeah I'll buy that if nobody comes with a better idea

\sum_{n=1}^\infty \frac{(-1)^n}{n^{n+\frac1n}} I want to use the alternating series test to show that this is conditionally convergent (it already fails absolute convergence). It's clear that the relevant terms will be positive and I can prove that they limit off to 0, but how do I prove that...