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Mega A Level Maths Thread MK II watch

1. (Original post by joostan)
DJ Set a slightly harder version of this on the old thread.
Prove by induction that:
Yeah I'm still quite stuck :-/ I got to this part but I can't see how to prove they're the same.

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2. (Original post by MathsNerd1)
Yeah I'm still quite stuck :-/ I got to this part but I can't see how to prove they're the same.

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Spoiler:
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Use the product rule
3. (Original post by DJMayes)
Well, I learned something new today.

And fair enough - this did come across very fishy from my perspective though.
Haha, fair do's, fair do's. ^.^

I probably would've done the same. xD
4. (Original post by joostan)
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One is always even, the other is always odd. So . . .
So its irrational?
5. (Original post by tigerz)
So its irrational?
Yarp
6. (Original post by joostan)
Yarp
Woohoo! thank you
7. (Original post by joostan)
Spoiler:
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Use the product rule
I'm still quite confused :-/ Sorry if its obvious but I just can't see how I can use that hint

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8. (Original post by joostan)
Yarp
Haha, yarp xD

(Original post by tigerz)
Woohoo! thank you
9. (Original post by MathsNerd1)
I'm still quite confused :-/ Sorry if its obvious but I just can't see how I can use that hint

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10. (Original post by MathsNerd1)
I'm still quite confused :-/ Sorry if its obvious but I just can't see how I can use that hint

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This is how you can use the product rule to derive the derivative of using the product rule and only the derivative of x. Can you extend this to a general case in your inductive step?
11. (Original post by Felix Felicis)
Haha, yarp xD
Gotta love Hot fuzz.
(Original post by tigerz)
Woohoo! thank you
NP
12. (Original post by DJMayes)

This is how you can use the product rule to derive the derivative of using the product rule and only the derivative of x. Can you extend this to a general case in your inductive step?
Oh okay, I think I can do that, let me just try it out

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13. (Original post by Felix Felicis)
Haha, yarp xD

Interesting one:

Spoiler:
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Assume the opposite - rational plus irrational = rational

We can then re-arrange to get rational minus rational = irrational

But the LHS is the rational so the RHS must be rational, which is a contradiction,so a rational plus an irrational must be irrational, as required.

14. (Original post by DJMayes)
Interesting one:

Spoiler:
Show

Assume the opposite - rational plus irrational = rational

We can then re-arrange to get rational minus rational = irrational

But the LHS is the rational so the RHS must be rational, which is a contradiction,so a rational plus an irrational must be irrational, as required.

Indeed Although not that interesting if you cracked it in 2 mins Just trying to think of random ones off the top of my head

Irrational + Irrational = Irrational <== True or false?
15. (Original post by DJMayes)
Interesting one:

Spoiler:
Show

Assume the opposite - rational plus irrational = rational

We can then re-arrange to get rational minus rational = irrational

But the LHS is the rational so the RHS must be rational, which is a contradiction,so a rational plus an irrational must be irrational, as required.

I think someone should make a thread for these types of questions.
16. (Original post by joostan)
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Got it thanks to everyone's help

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17. (Original post by MAyman12)
I think someone should make a thread for these types of questions.
See that's what the proof is trivial is for but tbh, most people on that thread would decimate these problems within femtoseconds and as AS maths is finished now, it's only A2 candidates left so this thread's died down a bit, so we may as well use it for these lighter problems
18. (Original post by Felix Felicis)
Indeed Although not that interesting if you cracked it in 2 mins Just trying to think of random ones off the top of my head

Irrational + Irrational = Irrational <== True or false?
Spoiler:
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True, because Pi+Pi=2Pi=Tau which is irrational. But then when I asked if, e+pi=irrational number, you said that it's impossible to know
19. Could anyone give me another question because I'm starting to get back into the mindset for them

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20. (Original post by MAyman12)
I think someone should make a thread for these types of questions.
(Original post by DJMayes)
Interesting one:

Spoiler:
Show

Assume the opposite - rational plus irrational = rational

We can then re-arrange to get rational minus rational = irrational

But the LHS is the rational so the RHS must be rational, which is a contradiction,so a rational plus an irrational must be irrational, as required.

Apologies for the ambiguity, I meant:

irrational + irrational = irrational for all irrational numbers <==== true or false?

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