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    Limiting Sum Help

    It is not true to say that a series must converge because it decreases (consider 1, 0, -1, -2, ...) nor that an increasing sequence must diverge (consider -1, -0.5, -0.25, ...) Even for a GP, a sequence may alternate and still approach a limit (such as the series 1, -0.5, 0.25, ...), or not...
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    The second equation here, -\cos{x} + 3 = 2 \implies \cos{x} = 1 is solvable, though
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    Help pls

    For part (c): Let the GP have a first term a. S_n = T_1 + T_2 + T_3 + ... + T_n = a + ar + ar^2 + ... ar^{n-1} = \frac{a(r^n - 1)}{r - 1} \begin{align*} R_n &= T_{n+1} + T_{n+2} + T_{n+3} + ... + T_{2n} \\ &= (T_1 + T_2 + T_3 + ... + T_n) + T_{n+1} + T_{n+2} + T_{n+3} + ... + T_{2n} - (T_1 +...
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    Help pls

    For (b): Let the common first term of the series be a. S_n = a + ar + ar^2 + ... + ar^{n-1} = \frac{a(r^n - 1)}{r - 1} \Sigma_n = a + ar^2 + ar^4 + ... + ar^{2n-1} = \frac{a(r^{2n} - 1)}{r^2 - 1} \begin{align*} \frac{\Sigma_n}{S_n} &= \frac{a(r^{2n} - 1)}{r^2 - 1} \div \frac{a(r^n - 1)}{r -...
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    Can you see what is wrong with this question?

    For f(x) to be a PDF, we require \int_{-\infty}^{\infty} f(x) \, dx = 1 \begin{align*} \text{Here, we have LHS } &= \int_{-\infty}^{\infty} f(x) \, dx \\ &= \int_{-\infty}^{0} 0 \, dx + \int_{0}^{2} \frac{4}{5} x(2 - x) \, dx + \int_{2}^{\infty} 0 \, dx \\ &= 0 + \frac{4}{5} \int_{0}^{2} 2x -...
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    Hard Proofs Question

    Very interesting, thanks for sharing. I agree that Stolz-Cesaro is definitely well outside the syllabus. I also note that the binomial theorem part is outside the syllabus as they only cover cases where n is a positive integer.
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    The solution to HSC 2020 Mathematics Advanced Q37

    You might want to update this, you are talking about Q31 not Q37
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    BoS trials Maths and Chemistry 2020

    Thanks... though look to the next post covering the 2020 HSC where I think failing to extrapolate will be penalised. As for the Chemistry BoS trial, that was all Jazz's work. I have offered him some feedback on some minor issues, but overall it was definitely excellent. :)
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    HSC Chemistry SOLUTIONS / Thoughts / Predictions

    I have just posted a long comment on Q25 of the 2020 HSC, the citric acid / sodium hydroxide question with the temperature v. volume graph in it. I have also discussed (in the same thread)...
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    BoS trials Maths and Chemistry 2020

    Now, MrGresh, you go to ask a question. It is very much not being a doofus - first, because it is always good to ask questions, and second, because you are right and have highlighted a point where Jazz has made a small error, and even his answer doesn't entirely address it (Sorry, Jazz): I...
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    BoS trials Maths and Chemistry 2020

    This is an interesting discussion, about which I would like to make a few points. Though I am not generally into arguments from claimed expertise, I do want to preface this by saying: I have a first class Honours degree with a double major in Chemistry and a minor in Mathematics I also have a...
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    Sequence Q.

    Thank you :)
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    Can you see what is wrong with this question?

    Looks like it fails the second condition
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    Hardest Maths Advanced Paper (2008-2019)

    Don't rely entirely on the Excel crosses, there are definitely some tat are wrong (at least in the MX1 book).
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    Perms and Coms question

    I'm tempted to say that the piece of paper's thickness has not changed. The stack of folded paper is much thicker than was the single, unfolded, sheet... but the single sheet remains the same thickness no matter how many times you fold it....
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    Sequence Q.

    You were? :confused:
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    Find the sum of the first 10 terms of the sequence 3+7+13+...

    Maybe if the question said that the sequence was the sum of an AP and a GP... or better, if its an AP + a GP where d=r...
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    Sequence Q.

    Note that there are several ways the answer could have been written, including: (-1)^{n-1}n (-1)^{n+1}(n+1)+(-1)^n (-1)^n(n+1) if you started at n=0 I could make the MCQ harder by making (C) (-1)^nn, which gives the sequence -1, 2, -3, 4, ... and (D) be a correct answer and see how many...
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    Is Tutoring really necessary

    Necessary? No. Helpful? Potentially - if the student is engaged and looking for help and the tutor has the skills to help that individual. I have done a lot of tutoring as the tutor and have had some very successful students, but I have also had students with whom I was not a good fit, in...
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    HSC Chemistry SOLUTIONS / Thoughts / Predictions

    Hi Jazz, It's great to be posting up solutions, but can you put a copy of the questions up too? Thanks.