Mega A Level Maths Thread MK II

Haha, yarp xD


How about this? Prove that a rational number + irrational number = irrational

Could anyone give me another question because I'm starting to get back into the mindset for them


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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

Prove $n! > 2^{n}$ for $n \geq 4, \ n \in \mathbb{Z^{+}}$

Apologies for the ambiguity, I meant:

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

Okays Can I just use any two numbers and prove using that?

Do you just want an answer or a proof as well?

No, you can't use specific examples

So I would use x? or w/e

Yeah

Prove $n! > 2^{n}$ for $n \geq 4, \ n \in \mathbb{Z^{+}}$

Can I just be incredibly lazy and say,

As imagined the inductive step has just baffled me, I don't know how to show the RHS being less than the LHS in a case of K+1

Apologies for the ambiguity, I meant:

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

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?

There is absolutely no need for induction.

Same difference