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Mega A Level Maths Thread MK II

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Original post by Robbie242
Hmm pondering on how to get the result root 10 other than that assumption/test, how would I necessarily be able to evaluate that, if its 1-r on the denominator for sinfinity for x/root 10 then that would equal 0 and thats bad. Hmm I'm not entirely sure, any hints felix?

And also its the sum to infinity to this suggests 1+1+1+1.... with roots blahblah which certainly can't equal 1

The sum isn't equal to root10. :tongue: Also, can I point out guys, you can't evaluate this using the infinite geometric series formula because each successive term is inside a new radical :redface:

You just need to evaluate 1+1+1+...\sqrt{1 + \sqrt{1 + \sqrt{1 + ... }}} and you're done - the answer isn't root 10 but it is root 10 * something (which is what you need to evaluate)
Original post by Felix Felicis

Spoiler



So you took sqrt10 as common factor which left you with phi so the answer is phi*sqrt10. I could've never thought about that. Genius
Original post by tigerz
I swear it simplifies as you go along?

Felix your maths questions are just one of a kind lols


Not sure tbh :redface:

I do like them though, pushing me away from A-level learning at least, I'll never be told to prove something by induction or show that (equation or something is given by) at an interview :tongue:
(edited 10 years ago)
Original post by Felix Felicis
The sum isn't equal to root10. :tongue: Also, can I point out guys, you can't evaluate this using the infinite geometric series formula because each successive term is inside a new radical :redface:

You just need to evaluate 1+1+1+...\sqrt{1 + \sqrt{1 + \sqrt{1 + ... }}} and you're done - the answer isn't root 10 but it is root 10 * something (which is what you need to evaluate)



Stupid question but how would I evaluate such a thing, if it goes on until infinity lol
Reply 3264
Avatar for tigerz
tigerz
Original post by MathsNerd1
Indeed as I could only imagine how much the question was annoying you and yeah, I tend to do that all the time but now I'm purposely trying to make an easier question harder for some sheer fun :tongue:


Yeah it was, thank you btw :smile: haha enjoy
Its difficult trying to jump between the two subjects >.<
Original post by Robbie242
Stupid question but how would I evaluate such a thing, if it goes on until infinity lol

Can you see a repeating unit anywhere inside the first square root? Try setting it equal to 'y' or something

(Not a stupid question btw, that's the whole point of the question :tongue: )
Original post by MAyman12
So you took sqrt10 as common factor which left you with phi so the answer is phi*sqrt10. I could've never thought about that. Genius

Well, that's what makes it a problem rather than an exercise. :biggrin:
Original post by Felix Felicis
Can you see a repeating unit anywhere inside the first square root? Try setting it equal to 'y' or something

(Not a stupid question btw, that's the whole point of the question :tongue: )


1 ? :s
Reply 3268
Avatar for tigerz
tigerz
Original post by Robbie242
Not sure tbh :redface:

I do like them though, pushing me away from A-level learning at least, I'll never be told to prove something by induction or show that (equation or something is given by) at an interview :tongue:


Yeah defo! its interesting

And ohh! it uses the same concept as the first question he set!!!
Original post by Robbie242
1 ? :s

Hint

Spoiler

Original post by tigerz
Yeah it was, thank you btw :smile: haha enjoy
Its difficult trying to jump between the two subjects >.<


Its fine, I just like to help out others :smile: And yeah, it really is that's why I'll be glad later on in the year that I'll only be doing Maths for the next 4 years :tongue:
Reply 3271
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tigerz
Original post by MathsNerd1
Its fine, I just like to help out others :smile: And yeah, it really is that's why I'll be glad later on in the year that I'll only be doing Maths for the next 4 years :tongue:


awwh :smile: Haha unless you also do a maths based job :wink: Then you'll be doing it for a while!
But I get what you mean
Original post by Felix Felicis
Hint

Spoiler



I don't know if this is a stupid suggestion 2\sqrt 2 ?

I don't know how exactly you'd square it lol, does it just get rid of the large sqrt surrounding the whole thing?

i.e.
Unparseable latex formula:

y^2=1+\sqrt{1+{\sqrt {1}+{\sqrt{1}+....}}}}}

(edited 10 years ago)
Original post by Felix Felicis
...


Teach me your ways oh great one :tongue:
Original post by Felix Felicis
Well, that's what makes it a problem rather than an exercise. :biggrin:


But how is the nested square roots equal phi?
Original post by tigerz
awwh :smile: Haha unless you also do a maths based job :wink: Then you'll be doing it for a while!
But I get what you mean


Well who knows it really depends on how I find it all at university :tongue: It should be some great fun though :biggrin:
Original post by Robbie242
I don't know if this is a stupid suggestion 2\sqrt 2 ?

I don't know how exactly you'd square it lol, does it just get rid of the large sqrt surrounding the whole thing?

No xD Squaring it once would get rid of the biggest square root, yes :biggrin: After that, it should fall out nicely

Original post by MathsNerd1
Teach me your ways oh great one :tongue:

I'm not all that. xD

Original post by MAyman12
But how is the nested square roots equal phi?

What's 1+1+1+...\sqrt{1 + \sqrt{1 + \sqrt{1 + ...}}} ? :tongue:
Reply 3277
Avatar for tigerz
tigerz
Original post by MathsNerd1
Well who knows it really depends on how I find it all at university :tongue: It should be some great fun though :biggrin:


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

I'm not all that. xD


Still you're better than me so I'd like to learn from you and others to help me improve my mathematical ability :biggrin:
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:


2\sqrt{2}? Why isn't it infinity its sqrt1 + sqrt1 infinite times, just why?
(edited 10 years ago)

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