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lol anyway I don't think all students can detect the errors

lol to see whether students can see the errors in these questions, which are not made by me but I found from other resources like past papers or books

nice. so my next question is $ If the series $ 2p-6p^2+18p^3-\cdots $ has a limiting sum, what values can its limiting sum be ? $

The questions are easy but wait do you really reckon you have solved them? $ Q1. Evaluate $ \log_a50 $ if $ \log_a5=1.3 $ and $\log_a2=0.43. $ Q2. Find the value of $ p $ if the limiting sum of the series $ 2p-6p^2+18p^3-54p^4+\cdots $ is $ \frac{4}{7}.

Re: HSC 2015 3U Marathon new question $ Find the volume of the solid generated when the region enclosed by the curves $ y=\frac{\sqrt{x}}{x+1}, y=\frac{1}{2\sqrt{x}} $ and the line $ x=4 $ is rotated about the $ x-$axis. $

Re: HSC 2015 2U Marathon new question $ Find the area enclosed by the curve $ y=\frac{1}{x}, $ the line $ y=2-x, $ the $ x-$axis, and the line $ x=4.

maximum means y value not x value

Re: How to solve this vector problem? do u know how to resolve a vector along othogonal directions? u resolve the velocity of the plane along positive x and positive y directions, find the component in positive y direction, this component needs to be equal to that of the wind, from which you...

Re: HSC 2015 4U Marathon \sec\alpha=\frac{\sec^2\alpha+\sec\alpha\tan\alpha}{\sec\alpha+\tan\alpha}

Re: HSC 2015 3U Marathon lol I simply used the wrong formula for the method of separator ( i used (m+n)!/m! instead of (m+n)!/m!/n! ) what i did is, suppose box 1 contain 2 coins, box 2 contains 4 coins, box 3 contains 6 coins and cup 4 contains 8 coins. now i need to take out four coins from...

Re: HSC 2015 3U Marathon I got 6!/4!+5!/3!+4!/2!=62

Re: HSC 2015 3U Marathon new question-repost my last one $ Prove by mathematical induction that $ 1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\codts+\frac{1}{2n-1}-\frac{1}{2n}=\frac{1}{n+1}+\frac{1}{n+2}+\cdots+ \frac {1}{2n}.

it is good to separate the whole sum into two parts. one of them is a GP, for which there is an "r", but the other is an AP, for which there is a "d", not an "r"

Re: HSC 2015 4U Marathon - Advanced Level s1 is not equal to b1 ?

Re: HSC 2015 3U Marathon lol as far as i know there is no shorter way, like there is no general formula for \sum_{k=1}^n\sin^{-1}(\sin k).

Re: HSC 2015 3U Marathon next one $ Find the exact value of $ \sum_{n=1}^{10}\sin^{-1}(\sin n).

Re: HSC 2015 4U Marathon - Advanced Level new question $ Two sequences $ \{a_n\} $ and $ \{b_n\} $ are such that (i) $ a_1=1 $ (ii) $ a_n $ and $ a_{n+1} $ are roots of the equation $ x^2-b_nx+2^n=0 $ for $ n=1, 2, 3, \cdots. $ Find the $n$th partial sum $ S_n $ of the sequence $ \{b_n\}.

Re: HSC 2015 3U Marathon new question $ Find $ \int2^{\ln x}dx.

Re: HSC 2015 3U Marathon there is a flaw when proving by induction, can you find it? ;) this is a very good example that shows how to fully understand the logic behind induction.

Re: HSC 2015 4U Marathon - Advanced Level it is clear that the trapezium is isosceles and angle ACD=angle BCD=30 degree. So angle BOC=60 degree and triangle BOC is equilateral. Note that the centre O must lie inside the trapezium. Let the radius=R and angle OCD=\alpha...