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  1. hey buddy what do you study? maths geek?
  2. You get upset over the strangest things.
  3. Hey, I noticed apost where u mentioned a friend that got a chem eng offer with a medicine personal statement? is he on student room ? its just becos im probly gonna do the same thing and could use some advice. any help would be appreciated, thanks
  4. Once you've found something which is bigger than the one you're aiming at, it does not matter which method you would use to prove that the bigger thing is less than the required value.

    It is perfectly acceptable to show inductively that something bigger satisfies the proposition, which you're asked to prove by induction.
    In fact, it is a common trick which I often see in many articles and proofs that I read, since clever people prefer to do "easy" jobs.

    It is evident that the induction for the proposed bigger series will be nearly the same.

    Btw, do you know how Euler proved that \displaystyle \sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}?
    I think you would enjoy that.

    My prep is going well, but I'm spending far more time than I should on Group Theory, Analysis and olympiad problems.
    This is going to change soon, however, since if I'm going to do the exam, I want to get a reasonable grade on it.
  5. Hi! How's your preparation going? I hope by June you'll be ready for SS.

    If you want to help this guy with the induction, certainly do.
    However, I think he should try some easier sums first to get the hang of the induction.

    Proof of \displaystyle \sum_{n=2}^{N} \frac{1}{n^2} < 1


    We observe that (n + 1)^2 > n(n + 1) and hence deduce that

    \displaystyle \sum_{n=2}^{N} \frac{1}{n^2} < \sum_{n=2}^{N} \frac{1}{n(n - 1)} = 1 - \frac{1}{N} < 1

    for every positive integer N greater than 2 and finite.

    Therefore, we make the inductive hypothesis that \displaystyle \sum_{n=2}^{N} \frac{1}{n^2} < 1 - \frac{1}{N} for every N \geq 2.

    The base case is obvious, so we continue by assuming that it is true for some k.
    To complete the induction we add the next term.

    \displaystyle \sum_{n=2}^{k} \frac{1}{n^2} + \frac{1}{(k + 1)^2} \ < \ 1 - \frac{1}{k}+ \frac{1}{(k + 1)^2}

    Hence, by the observation from above.

    \displaystyle \sum_{n=2}^{k + 1} \frac{1}{n^2} \ < \ 1 - \frac{1}{k} + \frac{1}{k(k + 1)} \right)

    Finally, we have.

    \displaystyle\ \ \ \ \ \ \ \ \ \ <  1 - \left(\frac{1}{k} - \frac{1}{k(k + 1)} \right)

    \displaystyle\ \ \ \ \ \ \ \ \ \ <  1 - \frac{1}{k + 1}

    We're done.

    If you want to read up more on induction - this below is your article, and it comes from here.
    Induction - Richard Earl, Oxford.
  6. hi
  7. hi dexter's laboratory.
  8. Congratulations for your Cambridge offer Just wondering, as I am considering applying to similar unis to you next year (Cambridge, Imperial, Warwick, Bath/Durham/UCL), what were the outcomes to your applications to the other unis?

    Also if possible, could you link me to the LSE page for maths? Do they do straight maths there?? or did you apply for maths with some other subject? When i looked on the site a couple of days ago I didn't come across maths on its own

    Thanks and well done again
  9. Hey!congratsss on ur offer?
    I look up to such students?can you please tell me what were your grades in gcse and what subjects in a levels so i can also follow your footsteps.
  10. hey, have you heard from cambridge?

About Me

  • About Intriguing Alias

    Where I study
    University of Cambridge
    Academic Info
    GCSEs: 6 A*s and 5 As
    AS Levels: AAAAAA
    A-Levels: A*A*A

    Firmed Cambridge Maths
    Insured Warwick Maths & Physics

    Declined UCL, Bath and LSE (w/ Econ) for maths.

    Currently studying Maths at Cambridge.

    If you want to know anything else like specific subjects of grades, UMS etc. feel free to PM.

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  • Join Date 27-06-2010

Age 20

Location Yorkshire

Join Date 27-06-2010

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