i think the phrasing of the question suggests the "telepath" came up with the dark haired hypothesis after the experiment. it isn't explicit, it only suggests this. GCSE science questions about experiments are often phrased in chronological sequence. my guess (and I've never marked GCSE science...
it's not if you go on to test that hypothesis with new data, but it is if you use the data you looked at to come with the hypothesis to prove the hypothesis.
the question implies the dark haired hypothesis comes after the experiment and so this is bad science. the students will get marks if they spot this.
this is what i understand it to mean (and i have taught GCSE science in the UK)
you missed some brackets/ that limit doesn't have to give 1. you've forgotten your own question, the product of two succesive (so even and odd) terms has to limit to 1
and StatusX a big thankyou for formalising my intuition, if that's what you did (hungover)
and OP I'm unsubscribing. if...
in fact if you set odd terms to just be 1/even terms you get a_n*a_n+1 = 1 or a_n * a_n+1 = (2 + i/p)/(2+(i-1)/p) = (2p + i)/(2p + i-1) which definitely limits to 1. you also have to take care of the "corners" of the oscilation, but i don't see these being a problem
another even subsequence that might do it. 2, 3, 2 1/2, 2, 2 1/3, 2 2/3, 3, 2 3/4, 2 1/2, 2 1/4, 2, 2 1/5, 2 2/5, 2 3/5, 2 4/5, 3, etc
set the odd members appropriately
i'm taking that a_n+1 to be the n+1 term of the sequence, not the n term plus 1
like i say i haven't done an epsilon delta proof as the manipulation is messy. i just took it as far as mathematica would go in reasonable time and got it limiting to 1. certainly not a proof, just a good...
no it's great that 16 year olds are being taught to recognise bad science. iirc gcse science is big on hypothesis testing and other basic principles of science
i dunno. it looks like it does, but you need to do the legwork, it's your quiz. it's probably easier to define a similar sequence in a more awkward way that makes working out the product limit easier. the idea is that even terms follow a non convergent path (such as sin wave) but with terms ever...
i always wondered how pressure as a function of depth was affected by irregular containers. i keep thinking of sensible ways to calculate it that give absurd results in certain configurations
i'm not sure if experiment is that relevant as we're asking if all time is within GR, a model, not whether GR's view of time (whether all or not) models reality correctly.