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    (Original post by Gilo98)
    do 15 and 6 share a common power? on reflection that is perhaps a useless question....
    clearly they do ...

    you have to move away from whole numbers
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    (Original post by TeeEm)
    clearly they do ...

    you have to move away from whole numbers
    Is it that obvious?


    ________________


    15/2.5=6
    square root of 6.25=2.5

    ??
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    (Original post by Gilo98)
    Is it that obvious?
    not at all...

    it is a very hard AS question
    (*****) in my scale.

    Believe it or not there are some people here that find these questions too easy (because of their preparation for STEP/AEA/BMO) so I put the "extras" just for them.

    Try it tomorrow when you are fresh
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    (Original post by TeeEm)
    not at all...

    it is a very hard AS question
    (*****) in my scale.

    Believe it or not there are some people here that find these questions too easy (because of their preparation for STEP/AEA/BMO) so I put the "extras" just for them.

    Try it tomorrow when you are fresh
    I will save it for saturday when I can sit down and do it properly.....will the solution be up by then? to think that by the end of the year I need to be finding this Q easy.....
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    (Original post by Gilo98)
    I will save it for saturday when I can sit down and do it properly.....will the solution be up by then? to think that by the end of the year I need to be finding this Q easy.....
    I put the solution up after 24 hours, so yes
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    (Original post by TeeEm)
    not at all...

    it is a very hard AS question
    (*****) in my scale.

    Believe it or not there are some people here that find these questions too easy (because of their preparation for STEP/AEA/BMO) so I put the "extras" just for them.

    Try it tomorrow when you are fresh
    Lol the extra is easier than the normal one
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    (Original post by Gome44)
    Lol the extra is easier than the normal one
    I wrote these questions in a hurry last night and the "normal" one is silly as it has a vital piece of information missing, though many of us might assume it.

    here is the correct version.

    Apologies
    Attached Images
  1. File Type: pdf Q17, Thursday 16-07-15.pdf (12.9 KB, 52 views)
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    27 days to A level results

    Question for Friday 17/07/15
    AS Maths Upwards
    (a few messy surd questions coming up as I wrote 4 today)

    and for those who want that little bit extra, a mathematical novelty
    ....
    maybe not quite a question as it is very hard to see what to do, so maybe a bit of research to complete this proof
    EDIT look for hint in post 790
    Attached Images
  2. File Type: pdf Q18, Friday 17-07-15, solution.pdf (68.7 KB, 62 views)
  3. File Type: pdf Q18, Friday 17-07-15,.pdf (11.3 KB, 84 views)
  4. File Type: pdf Q18, Friday 17-07-15, EXTRA solution.pdf (149.7 KB, 63 views)
  5. File Type: pdf Q18, Friday 17-07-15, EXTRA.pdf (8.4 KB, 50 views)
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    (Original post by TeeEm)
    27 days to A level results

    Question for Friday 17/07/15
    AS Maths Upwards
    (a few messy surd questions coming up as I wrote 4 today)

    and for those who want that little bit extra, a mathematical novelty
    ....
    maybe not quite a question as it is very hard to see what to do, so maybe a bit of research to complete this proof
    l acknowledge that when I awaken I shall firmly regret this decision. However, drunk me shall accept this next challenge. An inebriated mathematician is truly useful/incompetent.

    morning edit: I don't recall typing this or seeing this question but as a mark of responsibility I shan't delete this post..for now.
    Spoiler:
    Show
    For the extra, I have no concrete idea how to do this but...
    For a non-terminating decimal expansion, which e of course has (I'm guessing this be assumed from the infinite series expression) can I say that all rational numbers with an infinite expression be expressed as the sum of one or more geometric series? i.e. 1/3 = 0.333333... so the sum of a geometric series with first term 0.3 and common ratio 1/10, 1/7 is 0.142857 recurring so we have the sums of 6 geometric series with common ratio (1/10)^6...
    The expansion of e apparently doesn't fit these criteria as each term is multiplied by a new unique reciprocal (I mean, you first have 1 (well, 2 I guess, as you have 1 + 1 first), then 1/2, then 1/3, then 1/4 and so on due to the factorial stuff)

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    (Original post by 13 1 20 8 42)
    l acknowledge that when I awaken I shall firmly regret this decision. However, drunk me shall accept this next challenge. An inebriated mathematician is truly useful/incompetent.

    morning edit: I don't recall typing this or seeing this question but as a mark of responsibility I shan't delete this post..for now.
    Spoiler:
    Show
    For the extra, I have no concrete idea how to do this but...
    For a non-terminating decimal expansion, which e of course has (I'm guessing this be assumed from the infinite series expression) can I say that all rational numbers with an infinite expression be expressed as the sum of one or more geometric series? i.e. 1/3 = 0.333333... so the sum of a geometric series with first term 0.3 and common ratio 1/10, 1/7 is 0.142857 recurring so we have the sums of 6 geometric series with common ratio (1/10)^6...
    The expansion of e apparently doesn't fit these criteria as each term is multiplied by a new unique reciprocal (I mean, you first have 1 (well, 2 I guess, as you have 1 + 1 first), then 1/2, then 1/3, then 1/4 and so on due to the factorial stuff)

    This is the general structure

    assume that e = p/q

    p/q = 1 + 1 +1/2! + 1/3! + 4! + 1/q! + 1/(q+1)! +...

    multiply by q!

    move some terms on the left

    LHS is a positive integer

    so RHS is a positive integer

    and somehow via inequalities and reasoning (usally found in mathematical analysis) the RHS is less than 1

    so we found a positive integer less than 1

    Contradiction
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    (Original post by TeeEm)
    This is the general structure

    assume that e = p/q

    p/q = 1 + 1 +1/2! + 1/3! + 4! + 1/q! + 1/(q+1)! +...

    multiply by q!

    move some terms on the left

    LHS is a positive integer

    so RHS is a positive integer

    and somehow via inequalities and reasoning (usally found in mathematical analysis) the RHS is less than 1

    so we found a positive integer less than 1

    Contradiction
    There is a way to do it with floorbased functions.


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    (Original post by physicsmaths)
    there is a way to do it with floorbased functions.


    posted from tsr mobile
    there are several proofs

    my question says "prove by contradiction"
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    I've noticed this thread has 40 pages. Sorry but what exactly is the purpose of this thread? I think we've established you're not Arsey
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    (Original post by kprime2)
    I've noticed this thread has 40 pages. Sorry but what exactly is the purpose of this thread? I think we've established you're not Arsey
    it is my office
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    (Original post by TeeEm)
    it is my office
    I see. So this is the place we come for your help?
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    (Original post by kprime2)
    I see. So this is the place we come for your help?
    No, but this is the thread on the background of my computer, when I am doing work in my actual office (except for another 2 weeks or so as I am on my holiday home in Greece).
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    (Original post by TeeEm)
    there are several proofs

    my question says "prove by contradiction"
    This way is by contradiction. Im on holiday but ikl see if i can write it up later. It is beauftiful it was in a previous step question.


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    (Original post by physicsmaths)
    This way is by contradiction. Im on holiday but ikl see if i can write it up later. It is beauftiful it was in a previous step question.


    Posted from TSR Mobile
    I will be truly interested to see it
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    (Original post by TeeEm)
    No, but this is the thread on the background of my computer, when I am doing work in my actual office (except for another 2 weeks or so as I am on my holiday home in Greece).
    Where in Greece out of curiosity?

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    (Original post by aersh8)
    Where in Greece out of curiosity?

    Posted from TSR Mobile
    It is in a nice strategic/geopolitical spot (best plot in Europe), alive, kicking and well.
 
 
 
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