hardest topic (2 Viewers)

[Raser]

you know what subscript means

a1
the 1 is the subscript

 

[Dumbarse]

subscript?? huh?

how does that affect the question or formula

 

[McLake]

Formula:

n /(1/a1 + 1/a2 + 1/a3 + ..... 1/an)

Explanation:

n is divided by the sum of fractions to n
[In the case where k = -1, for a HM]

 

[Raser]

each a is a different value
so from a1 to an
there are n values of a
if u still don't get it, someone else explain it

 

[Dumbarse]

semi get it,
whats an example, maybe that will help
this is much appreciated =]

 

[spice girl]

An example? try this:

Given a1 + a2 + ... + an = k, and a1, a2, ..., an > 0

Prove 1/(a1) + 1/(a2) + ... + 1/(an) >= (n^2)/k

 

[Raser]

my god spice girl do u have all these stuff in ur head
ur either got a god damn good memory or else i can't see how u can have a life =)

 

[spice girl]

You just reverse the process and answers become questions...it's not hard to make these things up...

and beside, these AM-whateverM inequalities often begin like: if a1 + a2 + ... + an = something, then blablabla..

 

[Raser]

do they??
i think i better start looking at inequalitie questions
or start praying they don't give us any

 

[Dumbarse]

cool ive got nothing, how do u do it??

 

[Dumbarse]

Originally posted by Raser
harmonic means
it's AM<=GM<=HM

i thought AM>=GM??

where does HM fit in..

 

[Raser]

oops sorry
it's the other way round

and go pick on someone else's mistakes

 

[spice girl]

Try AM >= HM

U prob don't need this in 4uHSC anyways...

 

[Weisy]

I like all this stuff, it's fascinating

but do we have to know harmonic mean at all for the HSC? It's only that it was never even mentioned to us.

Also in the example that spice girl gave, n is integral?

It would be great to see the proof of that example...I've tried, except I don't think my working's legal. And I've also never done a problem like it before.

 

[BlackJack]

Yeah, it's integral... n is the number of terms 'a'.

I haven't heard of HM before either. I wonder what it means... I don't think we'd need this in the HSC though, harmonic means aren't mentioned in the syllabus... (however, if they lead us up to a proof...)

 

[spice girl]

Knowing the harmonic mean isn't necessary, but in 4umaths, using any method is legal. Personally i've never used the harmonic mean crap, there's usually another way. But anyways:

a1 + a2 + ... + an = k

(a1 + a2 + ... + an)/n = k/n

You look at the expression: 1/(a1) + 1/(a2) + ... + 1/(an) and you recognise it as part of an HM expression. So you use AM >= HM:

(a1 + a2 + ... + an)/n >= n / (1/(a1) + 1/(a2) + ... + 1/(an))

k/n >= n / (1/(a1) + 1/(a2) + ... + 1/(an))
thus 1/(a1) + 1/(a2) + ... + 1/(an) >= (n^2)/k

 

[Raser]

well my teacher at school didn't mention HM either
but they taught us that in 3u at tutoring so i just thought it might pop up in 4u
anyway it's not likely we're gonna get everything done so might as well just skip it

 

[Weisy]

thank you