HSC Stuff > HSC Mathematics Extension 1
Induction Inequality
jamonwindeyer:
--- Quote from: RuiAce on January 13, 2017, 01:47:33 pm ---CUBES, Jamon!!!
--- End quote ---
Lol whoops
RuiAce:
--- Quote from: de on January 13, 2017, 02:02:29 pm ---I realise that this is supposed to be done with induction. However, I'll just mention a smoother method. You can just consider the equation modulo 3. Then you can sub 0,1,2 into the equation and since and and we are done.
*modulo means considering all numbers as their remainder when divided by 3.
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Modulo arithmetic is not taught in the HSC maths courses.
Else I would've used it.
Explanation to the curious ones though:
If you think about it. If you go back to Year 3 and you did long division with integers, if you divided something by 3 your remainder would be either 0, 1 or 2. Hence, every number must be said to be 0, 1, or 2 "modulo 3". The idea is to think only in terms of the remainder as it significantly reduces your cases.
It's one of the instances where proof by exhaustion is swifter than proof by induction.
de:
--- Quote from: RuiAce on January 13, 2017, 02:43:22 pm ---The idea is to think only in terms of the remainder as it significantly reduces your cases.
It's one of the instances where proof by exhaustion is swifter than proof by induction.
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Where "significantly" takes you from infinite to 3 cases (or even one if you think about it correctly)!
RuiAce:
It's good for looking at and learning something extra.
But if you used it in an exam, you'd lose marks. The HSC has become stricter over you sticking to only content taught in the course. Just remember that.
de:
--- Quote from: RuiAce on January 13, 2017, 04:29:48 pm ---It's good for looking at and learning something extra.
But if you used it in an exam, you'd lose marks. The HSC has become stricter over you sticking to only content taught in the course. Just remember that.
--- End quote ---
DW I'm from vic and have already finished! If we avoid discussing stuff external to the course on here we do foster an unnecessarily inward looking perspective. Remember I did provide the disclaimer of "this is supposed to be done with induction".
Also, in vic at least I was under the impression you can put down whatever is correct... providing you explain it properly (unless of course it specifies a method).
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