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    (Original post by Felix Felicis)
    :confused: You already solved this on post 3186 :confused:


    Look at the underbraced bit
    Yes, but that doesn't mean I understand the concept It's all equal to 1 at the end?
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    (Original post by tigerz)
    LOL, never type like that again. ever.

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    Just messing :P ofc we are, especially some of you clever ones haha, you guys fascinate me :clap2:
    Whatz wrong wit tlkin lyk dis Aha just kidding I'd never be caught dead talking like that in real life And I can only imagine how Felix will reply to this, if he does that is I wouldn't say I'm clever though as on TSR I'm pretty average really
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    (Original post by Robbie242)
    I got y=1+root 5 /2 from completing the square, please tell me I'm right

    then \dfrac{x}{\sqrt 10}=\dfrac{1+\sqrt 5}{2}

    therefore x=\dfrac{\sqrt 10 + 5\sqrt 2}{2}
    Correct

    (Original post by MAyman12)
    Yes, but that doesn't mean I understand the concept It's all equal to 1 at the end?
    (Original post by Robbie242)
    I got y=1+root 5 /2 from completing the square, please tell me I'm right

    then \dfrac{x}{\sqrt 10}=\dfrac{1+\sqrt 5}{2}

    therefore x=\dfrac{\sqrt 10 + 5\sqrt 2}{2}
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    (Original post by Felix Felicis)
    Correct
    Can you explain what phi is to me, apparently it has some importance here, and you constantly used it :P
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    (Original post by MAyman12)
    Felix this if for you This is a problem by Ramanujan so it is hard.
    I'll get back to you.
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    (Original post by Robbie242)
    Can you explain what phi is to me, apparently it has some importance here, and you constantly used it :P
    \phi = \dfrac{1 + \sqrt{5}}{2}

    It's just a number, like pi and it's just as important because it appears everywhere It's called the golden ratio if you're interested - you could think of it as being the positive root of x^{2} -x-1=0 - I kept using it for these questions because this equation keeps popping up a lot for these questions, hence phi keeps popping up a lot
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    (Original post by Felix Felicis)
    Woah, one at a time guys. :lol: More than enough Felix to go around :sexface:


    No xD Ok, you have y = \sqrt{1 + \sqrt{1 + \sqrt{1 + ... }}} \Rightarrow y^{2} = 1 + \displaystyle\underbrace{\sqrt{1 + \sqrt{1 + \sqrt{1 + ... }}}}_{\alpha}

    Does \alpha look familiar?
    LOOOL, Felix your so popular :giggle:
    I really wan't to give you a question you can't solve...BTW can you explain this question later on?d/w its not urgent
    (Original post by MathsNerd1)
    Whatz wrong wit tlkin lyk dis Aha just kidding I'd never be caught dead talking like that in real life And I can only imagine how Felix will reply to this, if he does that is I wouldn't say I'm clever though as on TSR I'm pretty average really
    Haha, 'in my ends' you'd be surprised at how many people talk like that >.<
    At school everyones like 'help me with this, how do you do that?' etc whereas on TSR, I feel so clueless, more like me asking for help!

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    (Original post by Felix Felicis)
    I'll get back to you.
    No problem. But can you explain the nested sqrt1 thingy?
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    (Original post by MAyman12)
    No problem. But can you explain the nested sqrt1 thingy?
    x = \sqrt{1 + \sqrt{1 + \sqrt{1 + ...}}} \Rightarrow x^{2} = 1 + \displaystyle\underbrace{\sqrt{1 + \sqrt{1 + \sqrt{1 + ...}}}}_{x} \Leftrightarrow x^{2} -x -1 = 0

    \Rightarrow x = \dfrac{1 + \sqrt{5}}{2} (we take the positive root as x &gt; 0)
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    (Original post by Felix Felicis)
    x = \sqrt{1 + \sqrt{1 + \sqrt{1 + ...}}} \Rightarrow x^{2} = 1 + \displaystyle\underbrace{\sqrt{1 + \sqrt{1 + \sqrt{1 + ...}}}}_{x} \Leftrightarrow x^{2} -x -1 = 0

    \Rightarrow x = \dfrac{1 + \sqrt{5}}{2} (we take the positive square root as x &gt; 0)
    Oh sorry I understand this but what I can't understand is how is that possible when the sqrt1 is simply 1?
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    (Original post by MAyman12)
    Oh sorry I understand this but what I can't understand is how is that possible when the sqrt1 is simply 1?
    But you're not taking just square root 1 :confused: You have repeating radicals here. Try testing it for small values of a finite series rather than the infinite...

    \sqrt{1 + \sqrt{1 + \sqrt{1}}} = \sqrt{1 + \sqrt{1 + 1}} = \sqrt{1 + \sqrt{2}}

    if you want a proof that it converges, then you may need to give me a bit more time.
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    (Original post by tigerz)
    Haha, 'in my ends' you'd be surprised at how many people talk like that >.<
    At school everyones like 'help me with this, how do you do that?' etc whereas on TSR, I feel so clueless, more like me asking for help!
    Well my 6th form is apparently in the second most deprived part of my area so I'm always bumping into people that talk like this and apparently at work I'm patronising people as I speak proper English and they just aren't familiar with it. Yeah that's exactly the same with me although I always ask for the challenge on TSR as I know that they can deliver
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    (Original post by Felix Felicis)
    \phi = \dfrac{1 + \sqrt{5}}{2}

    It's just a number, like pi and it's just as important because it appears everywhere It's called the golden ratio if you're interested - you could think of it as being the positive root of x^{2} -x-1=0 - I kept using it for these questions because this equation keeps popping up a lot for these questions, hence phi keeps popping up a lot
    Thanks! One thing, do I have to write down that annoying greek letter for phi, because I'm finding it literally impossible to write down neatly, would rather do that theta like thing
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    (Original post by Felix Felicis)
    But you're not taking just square root 1 :confused: You have repeating radicals here. Try testing it for small values of a finite series rather than the infinite...

    \sqrt{1 + \sqrt{1 + \sqrt{1}}} = \sqrt{1 + \sqrt{1 + 1}} = \sqrt{1 + \sqrt{2}}

    if you want a proof that it converges, then you may need to give me a bit more time.
    Oh okay take your time:yy: Sorry, if I'm asking too much
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    (Original post by Robbie242)
    Thanks! One thing, do I have to write down that annoying greek letter for phi, because I'm finding it literally impossible to write down neatly, would rather do that theta like thing
    Seriously? I would have thought that it would be one of the easier greek letters to write down :lol:

    I occasionally have trouble writing uppercase sigma neatly :erm:
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    (Original post by justinawe)
    Seriously? I would have thought that it would be one of the easier greek letters to write down :lol:

    I occasionally have trouble writing uppercase sigma neatly :erm:
    I find greek letters elegant and especially sigma
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    (Original post by MAyman12)
    I find greek letters elegant and especially sigma
    See I like sigma! there's a reason I have a laptop for the rest of my exams apart from maths
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    (Original post by MAyman12)
    I find greek letters elegant and especially sigma

    (Original post by Robbie242)
    See I like sigma! there's a reason I have a laptop for the rest of my exams apart from maths
    I sometimes write uppercase sigma using a ruler so that it comes out neatly :teehee:
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    (Original post by justinawe)
    Seriously? I would have thought that it would be one of the easier greek letters to write down :lol:

    I occasionally have trouble writing uppercase sigma neatly :erm:
    I can't write lowercase sigma as it ends up looking like a 6 o.O
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    (Original post by reubenkinara)
    I can't write lowercase sigma as it ends up looking like a 6 o.O
    my b's look more like 6's, so I hate when the two merge in one question I could mistakenly say b+6=r -> 2(6)=r herp derp, haven't done this in an exam yet thankfully
 
 
 
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