Results 1 to 8 of 8

Math Help - [SOLVED] Just a challenge question

  1. #1
    Newbie
    Joined
    Apr 2008
    From
    With the fairies
    Posts
    8

    Red face [SOLVED] Just a challenge question

    What is the value of √(2+√(2+√(2+...))) etc?

    This is just a challenge question for which I am curious about.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,

    Is it 2 ?

    Assuming that f(n+1)=\sqrt{2+f(n)}

    If L is the limit, then \lim_{n \to \infty} f(n+1)=\lim_{n \to \infty} f(n)=L

    L=\sqrt{2+L}

    --> L^2=2+L \Longleftrightarrow L^2-L-2=0

    The solutions to this are -1 and 2. But L has to be > 0.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2008
    From
    With the fairies
    Posts
    8
    It could be...I have no idea how to check it. Can you explain how you worked that out? Thanks.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    I edited

    This is, of course, assuming that the series converges.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Apr 2008
    From
    With the fairies
    Posts
    8
    Thanks for that...

    I, however, being an average tenth grader, do not understand that thing with the n+1 and the limit/infinity stuff. (basically, the entire explanation).

    I'm thinking that the n+1 is something got to do with a series of numbers of something...but otherwise, I don't understand it.

    If it helps, the challenge question provides a hint on how to start it:
    Let x be √(2+√(2+√(2+...))) and square both sides.

    If you could possibly explain it starting with a simpler method (for dummies), then perhaps I will be able to understand.

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Oh, sorry for that

    The n, n+1 thing means "the nth term of the sequence, etc..."


    Well, with the hint, I can explain better (I hope), and it's quite alike with my method but it will be more clear


    x=\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{\dots}}}}

    Square it :

    x^2=2+{\color{red}\sqrt{2+\sqrt{2+\sqrt{\dots}}}}

    Since the dots mean "infinity", the red part is also equal to x (this is, imho, the most difficult part of the process, so if you understand it, it's great )

    Hence x^2=2+x

    x^2-x-2=0

    The discriminant \Delta=1+8=9 (I don't know if you've already studied that, if not, complete the square )

    Thus the solutions are x_1=\dots, x_2=\dots

    But, since x is the square root of something, it has to be a positive number. This means that you can take only one of the solutions
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Apr 2008
    From
    With the fairies
    Posts
    8
    Oh, I understand it now.

    Thanks for your help


    (PS: How much time do you spend on this forum? Every time I ask a question, it's always you who replies so quickly )
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Quote Originally Posted by anne. View Post
    Oh, I understand it now.

    Thanks for your help


    (PS: How much time do you spend on this forum? Every time I ask a question, it's always you who replies so quickly )
    Oh really ?
    I know I spend too much time

    The fact that I answer is maybe due to most of people here are from the USA. Hence if you post, it's night for them
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Challenge question
    Posted in the Math Challenge Problems Forum
    Replies: 10
    Last Post: February 8th 2011, 10:47 AM
  2. Challenge Question no 1
    Posted in the Statistics Forum
    Replies: 1
    Last Post: July 8th 2010, 02:38 AM
  3. Challenge question
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: May 27th 2009, 12:03 AM

Search Tags


/mathhelpforum @mathhelpforum