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.
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...)
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:
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