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Original post by tigerz
Yeah, just see where you end up :P


That's the idea really, oh and meet some cool people and we all know that the cool people go on to study Maths :tongue:
Original post by Felix Felicis
No xD Squaring it once would get rid of the biggest square root, yes :biggrin: After that, it should fall out nicely


I'm not all that. xD


What's 1+1+1+...\sqrt{1 + \sqrt{1 + \sqrt{1 + ...}}} ? :tongue:



Ok so I've ended up with y2=1+1+1+1...y^2={1+\sqrt{1+\sqrt{1+\sqrt{1}...}}}

I'm out of ideas, It falls out to be a 1 and then 3 separate terms, do I need to focus on those 3 terms and sum them up? which gives me 1.553773974... am not sure though

Newton Raphson method has destroyed my common sense
(edited 10 years ago)
Reply 3282
Original post by MathsNerd1
That's the idea really, oh and meet some cool people and we all know that the cool people go on to study Maths :tongue:


Haha exactly, unless they're just doing maths for the sake of it, all the people that actually understand how interesting it can be are the :cool: ones
These questions take up so much space... I normally don't try them at all, because everyone else posts so many replies to them :lol:

Maybe I should join in... :nah:
Original post by tigerz
Haha exactly, unless they're just doing maths for the sake of it, all the people that actually understand how interesting it can be are the :cool: ones


Damn straight, that's why this forum is always so active cause we iz all cool blud :wink: lol
Original post by Robbie242
Ok so I've ended up with y2=y^2=

I'm out of ideas, It falls out to be a 1 and then 3 separate terms, do I need to focus on those 3 terms and sum them up? which gives me 1.553773974... am not sure though

Hmm I get
x2=1+1+1+1...x^2={1+\sqrt{1+\sqrt{1+\sqrt{1}...}}}
So (x21)=x(x^2-1)=x
Original post by L'Evil Fish
These questions take up so much space... I normally don't try them at all, because everyone else posts so many replies to them :lol:

Maybe I should join in... :nah:


Join in on the fun, they're pretty cool :tongue: Maybe you could even post one you find will be challenging too?
Original post by MathsNerd1
Join in on the fun, they're pretty cool :tongue: Maybe you could even post one you find will be challenging too?


I don't have anything challenging...
Reply 3288
Original post by MathsNerd1
Damn straight, that's why this forum is always so active cause we iz all cool blud :wink: lol


LOL, never type like that again. ever.

Spoiler

Original post by MAyman12
2\sqrt{2}? Why isn't it infinity its sqrt1 + sqrt1 infinite times, just why?

:confused: You already solved this on post 3186 :confused:

Original post by Robbie242
Ok so I've ended up with y2=1+1+1+...yy^2=1+ \displaystyle\underbrace{\sqrt{1 + \sqrt{1 + ...}}}_{y}

I'm out of ideas, It falls out to be a 1 and then 3 separate terms, do I need to focus on those 3 terms and sum them up? which gives me 1.553773974... am not sure though

Newton Raphson method has destroyed my common sense

Look at the underbraced bit :biggrin:
(edited 10 years ago)
Is it y^2=1+y?


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


Look at the underbraced bit :biggrin:


So then y^2 = 1 + y? Which you can then solve using quadratic formula :biggrin: (sorry, never used LaTex)
(edited 10 years ago)
Really neat. Wish I could be a maths genius too :3


Posted from TSR Mobile
Original post by Felix Felicis
:confused: You already solved this on post 3186 :confused:


Look at the underbraced bit :biggrin:


nvmnvmvnvmvnm
(edited 10 years ago)
Original post by Revengeissweet
Is it y^2=1+y?


Posted from TSR Mobile


Original post by Zaphod77
So then y^2 = 1 + y? (sorry, never used LaTex)

Haha, the more the merrier :biggrin: And yes :biggrin:
Original post by Zaphod77
So then y^2 = 1 + y? (sorry, never used LaTex)

That's what I got. Then just solve for y.
Original post by Felix Felicis
Haha, the more the merrier :biggrin: And yes :biggrin:

Makes sense now that I started again. Still not sure how you got from the series to the continuous fraction though ...
Original post by Felix Felicis


Felix this if for you:colone: This is a problem by Ramanujan so it is hard.
Woah, one at a time guys. :lol: More than enough Felix to go around :sexface:

Original post by Robbie242
1+21+\sqrt 2 ? or since your edit 1+1 = 2 ? lol im so baffled

No xD Ok, you have y=1+1+1+...y2=1+1+1+1+...αy = \sqrt{1 + \sqrt{1 + \sqrt{1 + ... }}} \Rightarrow y^{2} = 1 + \displaystyle\underbrace{\sqrt{1 + \sqrt{1 + \sqrt{1 + ... }}}}_{\alpha}

Does α\alpha look familiar?
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=1+1+1+...y2=1+1+1+1+...αy = \sqrt{1 + \sqrt{1 + \sqrt{1 + ... }}} \Rightarrow y^{2} = 1 + \displaystyle\underbrace{\sqrt{1 + \sqrt{1 + \sqrt{1 + ... }}}}_{\alpha}

Does α\alpha look familiar?


I got y=1+root 5 /2 from completing the square, please tell me I'm right

then x10=1+52\dfrac{x}{\sqrt 10}=\dfrac{1+\sqrt 5}{2}

therefore x=10+522x=\dfrac{\sqrt 10 + 5\sqrt 2}{2}
(edited 10 years ago)

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