September 25, 2023, 03:32:44 am

### AuthorTopic: MX1 topic tests questions with atarnotes proof test  (Read 3297 times) Tweet Share

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#### joengelman

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##### MX1 topic tests questions with atarnotes proof test
« on: April 15, 2020, 11:02:41 am »
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Hey guys,

Just curious, when doing the proof questions on the MX1 topic test, I've noticed that a lot of the series questions are just proving one thing? Like at my school, we've learnt to do questions in series, like 1+4+9+n=2n+1, not like prove x^k=(1-x^n)/1-x, where there are like two variables (being n and k within the same equations). Have I missed something? I mean, Maths in focus + New senior doesn't have those sorts of questions, but maybe I'm looking at the wrong textbooks?

Thanks,
Jo

#### RuiAce

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##### Re: MX1 topic tests questions with atarnotes proof test
« Reply #1 on: April 15, 2020, 02:03:29 pm »
+4
It's a sum.
$\sum_{k=1}^{n-1} x^k\text{ is a shorthand for }1+x+x^2+\dots+x^{n-1}.\\ \text{So in that question, what you're trying to prove by mathematical induction is the statement}\\ \boxed{ 1+x+x^2+\cdots+x^{n-1} = \frac{x^n-1}{x-1}}.$
Which happens to be the sum of terms in a geometric sequence. In particular, with first term $1$ and common ratio $x$.

Sigma notation is actually no longer a part of Adv/MX1 though - it's exclusively an MX2 concept. I told the author that just now so hopefully that issue will get addressed. For now though, I'd suggest just proving that equivalent statement I boxed instead.

(Note however that NESA allows use of sigma notation in MX1 as a shorthand convenience. It's just not taught explicitly.)