HSC Stuff > HSC Mathematics Extension 2
Mathematics Extension 2 Challenge Marathon
ellipse:
--- Quote from: RuiAce on September 08, 2017, 10:53:36 pm ---This question first appeared as a meme, ironically enough. At first glance, it looks ridiculous. But it's all about finding the right starting point...
I had a go, and I promise it's doable within MX2 boundaries.
--- End quote ---
its a telescoping series,
hence you'll end up with the first term (J_0/I_0) + the last term (J_n)/(I_n)
as n goes to infinity, the last term disappears (ill try to prove this later) so evaluating J_0 and I_0, we get pi^2/6
its interestingly the basel problem, and also appeared as the last q in 2010 mx2
RuiAce:
--- Quote from: ellipse on September 10, 2017, 05:01:24 pm ---its a telescoping series,
hence you'll end up with the first term (J_0/I_0) + the last term (J_n)/(I_n)
as n goes to infinity, the last term disappears (ill try to prove this later) so evaluating J_0 and I_0, we get pi^2/6
its interestingly the basel problem, and also appeared as the last q in 2010 mx2
--- End quote ---
Of course, the right idea.
Care to show some working out now? You wouldn't be able to say in an exam, by inspection, the last term vanishes.
Edit: Had a look, because I definitely remembered the π^2/6 in the 2010 exam. Didn't realise the final result was the same.
But pretty much as you alluded to there's a faster way than the 2010 exam method.
Paradoxica:
--- Quote from: RuiAce on July 21, 2017, 12:17:55 am ---
--- End quote ---
*briefly tries bashing*
*realises polar co-ordinates is faster*
*facepalms*
Shlomo314:
i guessing this is wrong because pythag can only be used on the real plane and the imaginary doesn't exist on the im plane?
RuiAce:
--- Quote from: Shlomo314 on October 30, 2017, 02:59:29 pm ---i guessing this is wrong because pythag can only be used on the real plane and the imaginary doesn't exist on the im plane?
--- End quote ---
Lol I saw this as a meme.
The fallacy is in that Pythagoras theorem uses lengths, so you need to take absolute values (moduli). It's a good joke though
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