What would you say the difficulty of this question is (2 Viewers)

[v.tex]

If this were in the hsc, what band would it be. I honestly don't know if its meant to be easy marks or somewhat hard (which i find it)

 

[C2H6O]

First part is very easy like part a i and ii. proving am-gm is sorta a standard proof but that's not to say its easy. the rest of this question is quite complex in that there's so many steps, but with practise it would get much easier. dont worry if it looks impossible though. to give a band estimate i would probably say e4. id recommend getting used to seeing the patterns such as where factorials can be pulled out from in proofs as well as other forms of representing arithmetic and geometric sums (look on formula sheet). btw i probably couldn't have solved this entire question when i did my hsc 4u and i still e4'd (though some who are smarter than me might say otherwise)

 

[C2H6O]

What i meant by recognising patterns is like if you have 1 + 2 + 3 + ... + n, this is equal to , and subsequently also equal to . Theres a chance that they then put n^2+n into a proof and you've gotta see that that's equal to 2(1+2+3+..n), as an example

 

[liamkk112]

View attachment 46400

If this were in the hsc, what band would it be. I honestly don't know if its meant to be easy marks or somewhat hard (which i find it)

b) is okay, not too difficult (though you'd probably not get told that what you're given is Jensen's inequality, you'd just get given the function and the inequality). c) is alright, as long as you can recognise that you'd have to take x_i=i in order to get the factorial. a) is a bit more difficult, namely iii) i'd say can be a bit hard to see at first. imo, the heron question you posted earlier is much harder, since there's much more tricky manipulation needed that you wouldn't be able to see quickly

as an aside, you can also prove am-gm with the cauchy-schwarz inequality and the dot product (inner product). imo that's the neatest, and easiest proof (as long as you can prove cauchy-schwarz, which especially for the dot product is easy)