Can you assume this identity? (1 Viewer)

[nick1048]

let m=1+x

mⁿ*mⁿ
m²ⁿ

surely you don't need any more than that.

Yea thats what I was just about to say, the beauty of maths is the us of replacment values. That's all the proof needs to be true.

 

[Rorix]

because its more true if we have one pronumeral instead of a pronumerial and a number or something...


(by inspection)

 

[Estel]

And hence we should offer a proof which uses a promumeral and a number.

 

[mojako]

nah, u gotta prove it by expanding each brackets using the binomial theorem
coz unless they say its given, then theyre testing to see if u know what binomial theorem is

oh please.....

you dont need to do that.
its a basic stuff which comes automatically by inspection

modifying what ngai said.. or taking my own forced and false interpretation of his post,
what he means is that you expand it to prove another thing.
you assume it's true, and you use the fact that its true to prove for another thing which is not as obvious as that. this other thing would be some kind of identity containing the nCr notation.
you use the fact that its true by expanding it using binomial technique.

If you see a question says: "Given that (1+x)^n (1+x)^n = (1+x)^(2n)",
it does so because the people who set the question don't want to directly tell you to use that result. By not telling you directly, there's a greater chance that you can't do the question.

 

[Archman]

hmm, it thought there is a very specialised and technical term for this type of stuff... cant remember damnit... oh i c, its called INDEX LAWS.

 

[mojako]

hmm, it thought there is a very specialised and technical term for this type of stuff... cant remember damnit... oh i c, its called INDEX LAWS.

really??
I dont think Ive heard that..

can somebody explain?

 

[mojako]

Well then (1+x)ⁿ isn't real.

And the other method would still be invalid.

no

(-1)^0.5 * (-1)*0.5 is still (-1)^(2*0.5) = -1

So Xayma's method is still valid.
And the binomial expansion method is invalid, because we can't have ^0.5C_k
well maybe we can, I just haven't seen it.
Now it's getting confusing... any help would be greatly appreciated.

 

[ND]

Just in case you were interested:

0.5Ck=0.5(0.5-1)(0.5-2)...(0.5-k+1)/k!

But it gets way harder with a non-integer k.

 

[mojako]

hmm.. interesting..
(no this time I'm being serious)

how can it be used? like to solve what problems?

BTW ND, if you don't mind...
a,b,c are sides of a triangle.
explain why (b-c)^2 <= a^2
Thanks.

 

[ND]

I've never actually used that in a question, i just remember cos i lecturer showed it as one way to solve a type of probability question (i don't think like anything you'll come across in 4u), but i prefer a different method.

Oh and for that question, think triangle inequality.

 

[ngai]

hmm, it thought there is a very specialised and technical term for this type of stuff... cant remember damnit... oh i c, its called INDEX LAWS.

but u mite lose marks if u use these "INDEX LAWS" coz examiners mite think uve skipped steps
i think its safe enough to prove it by expansion using the binomial theorem
but to be totally safe, u should really prove the binomial theorem first before using it

 

[Rorix]

can I assume the fundamental axioms of algebra, or should i state them first?

 

[Li0n]

no

(-1)^0.5 * (-1)*0.5 is still (-1)^(2*0.5) = -1

So Xayma's method is still valid.
And the binomial expansion method is invalid, because we can't have ^0.5C_k
well maybe we can, I just haven't seen it.
Now it's getting confusing... any help would be greatly appreciated.

but we don't do 4unit here (some anyway)
so how the hell would people know that i² = -1

 

[mojako]

but u mite lose marks if u use these "INDEX LAWS" coz examiners mite think uve skipped steps
i think its safe enough to prove it by expansion using the binomial theorem
but to be totally safe, u should really prove the binomial theorem first before using it

oh ngai...
too much influence from your 4U course
my friends doing 4U told me that they need to prove everything
including these obvious stuff
and most of them wanna quit but the teachers wont let them
thats my Im afraid of going into 4U in the first place.
no I do 4U and we dont have to prove everyhing

 

[mojako]

can I assume the fundamental axioms of algebra, or should i state them first?

out of interest, what are the fundamental axioms of algebra?
I can use google but I wont bother

 

[mojako]

but we don't do 4unit here (some anyway)
so how the hell would people know that i² = -1

I dont do 4U!
I just asked a 4U question to test ND's ability.

and what? i^2 = -1?
isn't i just a letter (or pronumeral in maths )
its like saying x^2 = -1..???

oh, I think I see what you mean... (after spending 10 minutes.. u waste my time!!)
I said (-1)^0.5 * (-1)^0.5 = [(-1)^0.5]^2
hmm.. r u saying that i = (-1)^0.5?
hmm... but isn't i just an ordinary pronumeral?

 

[Slidey]

You don't do 4 unit, Moj? I have to say you're the most confusing person ever.

 

[Xayma]

no

(-1)^0.5 * (-1)*0.5 is still (-1)^(2*0.5) = -1

So Xayma's method is still valid.
And the binomial expansion method is invalid, because we can't have ^0.5C_k
well maybe we can, I just haven't seen it.
Now it's getting confusing... any help would be greatly appreciated.

(-1)^0.5 isn't real. Like I stated. And it was withoutaface's method

And I think it is the gamma function you could find a generalisation for 0.5!

 

[mojako]

doesnt matter if its not real,
as long as the final result is real
(the final result is -1^2*0.5)

 

[ND]

I dont do 4U!
I just asked a 4U question to test ND's ability.

?
What do you mean?