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    (Original post by TheMagicMan)
    I remember doing a question exactly like this at some point... remind me where it comes from
    It's from an exam for some uni/olympiad in Asia, I think. (Got it from an old book at home...)

    THe solution:
    Spoiler:
    Show

    s_{n}=\sum_{k=0}^{\infty}(\frac{  n-1}{n!})(\frac{1}{n})^{k}

    So,  s_{1}=0\ or\ s_{n}=\frac{1}{(n-1)!} for n>1.

    Also, \sum_{n=1}^{100}|n^{2}-3n+1|S_{n}=\sum_{n=2}^{100}|n^{2  }-3n+1|S_{n}=1+\sum_{n=3}^{100}(n^  {2}-3n+1)S_{n}, as the n=1 term is zero, n=2 term is 1, and the term inside the modulus is postive for n>2.

    So the summation is \frac{100^{2}}{100!}+ \sum_{n=1}^{100}|n^{2}-3n+1|S_{n}=\frac{100^{2}}{100!}+  1+\sum_{n=3}^{100}(n^{2}-3n+1)S_{n}

    =\frac{100^{2}}{100!}+1+\sum_{n=  3}^{100}\frac{n^{2}-3n+1}{(n-1)!}

    =\frac{100^{2}}{100!}+1+\sum_{n=  3}^{100}\frac{(n-1)^{2}-n}{(n-1)!} =\frac{100^{2}}{100!}+1+\sum_{n=  3}^{100}\frac{(n-1)}{(n-2)!}-\frac{n}{(n-1)!}
    This telescopic sum cancels to leave

    \frac{100^{2}}{100!}+1+(2-\frac{100}{99!})=3
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    (Original post by Contrad!ction.)
    I wanted to do Stats GCSE - when we picked our options in Year 9 I chose Stats but the old head of maths was like 'oh, there's not enough maths teachers!' so I ended up doing Food Tech with an absolute ***** of a teacher who I hated and ended up getting a D.

    A phase I now regret
    Awww We had no maths choices in year 9 but still....thats very mean if you wanted to do it!!

    (Original post by Jampolo)
    Mathematics i hope, but because of the open-ness of the degree i would like to do financial mathematics as well, incase i go into finance
    Ooh cool that sounds good Theres a few places that do a specific finacial maths degree: i think lancaster, sheffield and somewhere else
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    (Original post by Contrad!ction.)
    I'll have that as the mock, I reckon my teacher'll fix the question then make up a mark scheme himself.

    That must have been annoying My teachers were brilliant with the coursework, I managed full marks somehow. I did a 18-page lab report on lenses and a presentation on the use of steel in the barrels of rifles but unfortunately I couldn't bring in any props for that one. A2 = 25-page lab report on the charge to mass ratio of an electron (we started the coursework on the week before FP1, meaning I had 3 exams to do whilst keeping on top of coursework) which was actually really interesting, although it took ages to get the equipment working. And I wasn't allowed to do it unsupervised because I was using ~5kV :cool:

    No money! :eek: Otherwise I'd have a 360 by now I've got a computer that I use for games occasionally but I need a new keyboard Cambridge does look nice but I don't think I'd be able to afford to get there Eww, I'm determined to do STEP, even if I don't get an offer needing it. But it'll take me a while because I'm trying to teach myself other stuff at the same time *is jealous of people who do A-Level Maths in Year 12*
    We had to do our coursework on internal resistance (Edexcel Salters Horners), ah it was horrible. We even visited a local power station for a competely irrelevant trip. Was fun though very dangerous place! I just used to hate going into lesson, it was all exam conditions and you couldn't ask the teacher anything otherwise marks were deducted! I got exactly 80%, so scraped an A :cool:
    We used one of them Van De Graaff generators in physics once, i used one in school but when my physics teacher told us they generate around 10,000 volts, i chickened out

    Ha, i don't do much with my computer. built it myself to play WoW, got bored then quit. Im a 360 kid :cool:. Aw but if its for an interview and a chance at getting in surely your parents will kindly offer? I want to do STEP, maybe AEA, but at the moment im just using AEA as practise for STEP. Good thing about STEP is that its written by OCR so its all the usual syllabus.

    EDIT : sorry for long reply, went out at 4 and literally just got in from playing football. I ache, alot.
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    (Original post by Rahul.S)
    safety nets? :confused: allow them moist talks
    loool ur wet.
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    (Original post by Jampolo)
    We had to do our coursework on internal resistance (Edexcel Salters Horners), ah it was horrible. We even visited a local power station for a competely irrelevant trip. Was fun though very dangerous place! I just used to hate going into lesson, it was all exam conditions and you couldn't ask the teacher anything otherwise marks were deducted! I got exactly 80%, so scraped an A :cool:
    We used one of them Van De Graaff generators in physics once, i used one in school but when my physics teacher told us they generate around 10,000 volts, i chickened out

    Ha, i don't do much with my computer. built it myself to play WoW, got bored then quit. Im a 360 kid :cool:. Aw but if its for an interview and a chance at getting in surely your parents will kindly offer? I want to do STEP, maybe AEA, but at the moment im just using AEA as practise for STEP. Good thing about STEP is that its written by OCR so its all the usual syllabus.

    EDIT : sorry for long reply, went out at 4 and literally just got in from playing football. I ache, alot.
    I'm probably one of the only people who can honestly say they're thankful for being on OCR B for Physics, I hate practical exams and tend to **** things up if I'm under pressure. So doing it in my own time was fine by me. Van De Graaff - if that's the one I think it is my old science teacher got someone to put their hands on it. Her hair was amazing after that

    Nah my parents have no money either, my dad's job's got no work to offer him so he's not been paid in a couple of months and I can't see it getting much better. Are there any C1/C2 friendly questions in the AEA? I want practice at the exam style, but haven't done much C3/C4.

    Love football, haven't played it in ages though. Used to be a defender for my school football team at one point.
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    (Original post by Contrad!ction.)
    Are there any C1/C2 friendly questions in the AEA? I want practice at the exam style, but haven't done much C3/C4.
    There's a few but it's mainly C3/4. Usually 1 or 2 logs and series qs per paper, iirc.
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    (Original post by Zuzuzu)
    There's a few but it's mainly C3/4. Usually 1 or 2 logs and series qs per paper, iirc.
    Ah cheers. I just want to have a go at some stuff now so I'm not rushing it once we do C4.
    Anyone who's only done as maths/further and is starting out with STEP, I'd recommend the 2004 paper, questions 1, 2, 3, 5 and 8 can be done with AS maths only.
    Just stumbled upon this whilst looking at the other pages. Awesome - which one?
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    (Original post by Contrad!ction.)
    I'm probably one of the only people who can honestly say they're thankful for being on OCR B for Physics, I hate practical exams and tend to **** things up if I'm under pressure. So doing it in my own time was fine by me. Van De Graaff - if that's the one I think it is my old science teacher got someone to put their hands on it. Her hair was amazing after that

    Nah my parents have no money either, my dad's job's got no work to offer him so he's not been paid in a couple of months and I can't see it getting much better. Are there any C1/C2 friendly questions in the AEA? I want practice at the exam style, but haven't done much C3/C4.

    Love football, haven't played it in ages though. Used to be a defender for my school football team at one point.
    I have really short hair so it sucks plus im not a fan of electric shocks anyway They scare me!

    aww god damn recession :rant: im surprised i still have a job Hmm theres not many, i find there to be more on STEP, mainly on co-ordinate geometry, and then some random questions on number theory.

    Ha this year i would have been playing football 10 years!! Long long time. But i work sundays so i need to get them changed
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    (Original post by Contrad!ction.)
    Ah cheers. I just want to have a go at some stuff now so I'm not rushing it once we do C4.

    Just stumbled upon this whilst looking at the other pages. Awesome - which one?
    Paper I 2004.
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    (Original post by twig)
    Here you go :

    Find the value of \frac{100^{2}}{100!}+ \sum_{n=1}^{100}|n^{2}-3n+1|S_{n}, where S_{n} is a G.P. with first term \frac{n-1}{n!} and common ratio \frac{1}{n}

    The question is quite fiddly/long, not anything neat as your one, but its the closest to a suitable series Q I could find. "Should" be quite straightforward (especially for you!).

    (I am terrible with Latex, so there could be an error btw...)
    I got:

    Spoiler:
    Show
    3

    The sum at the end took some time to figure out how they cancel... Nice question though, do you know where I could more like this?


    NVM... Didn't see it above lol
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    (Original post by Jampolo)
    loool ur wet.
    i leave girls wet....since im moist and your dry :sexface:
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    (Original post by Rahul.S)
    i leave girls wet....since im moist and your dry :sexface:
    loooool the closest you get to making a girl wet is a water fight..
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    do I need to call the Mods?
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    (Original post by ben-smith)
    do I need to call the Mods?
    Oh no, we mentioned girls on a maths thread. Theres a reason mathematics is regarded as a geeky subject..
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    (Original post by Jampolo)
    loooool the closest you get to making a girl wet is a water fight..
    if water fight means what i think it means :sexface: then yh
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    (Original post by Rahul.S)
    if water fight means what i think it means :sexface: then yh
    screw water fights. I make it rain :sexface:
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    (Original post by twig)
    It's from an exam for some uni/olympiad in Asia, I think. (Got it from an old book at home...)

    THe solution:
    Spoiler:
    Show

    s_{n}=\sum_{k=0}^{\infty}(\frac{  n-1}{n!})(\frac{1}{n})^{k}

    So,  s_{1}=0\ or\ s_{n}=\frac{1}{(n-1)!} for n>1.

    Also, \sum_{n=1}^{100}|n^{2}-3n+1|S_{n}=\sum_{n=2}^{100}|n^{2  }-3n+1|S_{n}=1+\sum_{n=3}^{100}(n^  {2}-3n+1)S_{n}, as the n=1 term is zero, n=2 term is 1, and the term inside the modulus is postive for n>2.

    So the summation is \frac{100^{2}}{100!}+ \sum_{n=1}^{100}|n^{2}-3n+1|S_{n}=\frac{100^{2}}{100!}+  1+\sum_{n=3}^{100}(n^{2}-3n+1)S_{n}

    =\frac{100^{2}}{100!}+1+\sum_{n=  3}^{100}\frac{n^{2}-3n+1}{(n-1)!}

    =\frac{100^{2}}{100!}+1+\sum_{n=  3}^{100}\frac{(n-1)^{2}-n}{(n-1)!} =\frac{100^{2}}{100!}+1+\sum_{n=  3}^{100}\frac{(n-1)}{(n-2)!}-\frac{n}{(n-1)!}
    This telescopic sum cancels to leave

    \frac{100^{2}}{100!}+1+(2-\frac{100}{99!})=3
    I thought you said it was long/fiddly hehe

    Seems to cancel nicely.
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    (Original post by Jampolo)
    screw water fights. I make it rain :sexface:
    how about a tsunami :sexface:
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    (Original post by Rahul.S)
    how about a tsunami :sexface:
    ooh kinky.. bet all the galdem love u
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    (Original post by Thrug)
    I thought you said it was long/fiddly hehe

    Seems to cancel nicely.
    I guess so, although I have no idea how I would have done it without the terms conveniently cancelling.

    Are you applying for maths this year? (If yes) Which unis are you looking into?
 
 
 
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