Results 1 to 5 of 5
Like Tree1Thanks
  • 1 Post By Plato

Math Help - Find the 2013th digit after the decimal point in the expression of...

  1. #1
    Newbie
    Joined
    Jan 2013
    From
    Japan
    Posts
    4

    Find the 2013th digit after the decimal point in the expression of...

    Let m=\frac{\sqrt{10^{4024}-1}}{3}
    Find the 2013th digit after the decimal point in the expression of \sqrt{m}



    It seems a similar problem.
    xkcd • View topic - math problem - driving me crazy
    But I don't think so. I can't write m to (\sqrt{a}+\sqrt{b})^n a,b,n is integer numbers
    Last edited by coriander; January 18th 2013 at 08:00 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,969
    Thanks
    1788
    Awards
    1

    Re: Find the 2013th digit after the decimal point in the expression of...

    Quote Originally Posted by coriander View Post
    Let m=\frac{\sqrt{10^{4024}-1}}{3}
    Find the 2013th digit after the decimal point in the expression of \sqrt{m}
    It seems a similar problem.
    xkcd View topic - math problem - driving me crazy
    But I don't think so. I can't write m to (\sqrt{a}+\sqrt{b})^n a,b,n is integer numbers

    Do you know the binomial series?

    Write \frac{\sqrt{10^{4024}-1}}{3}=\tfrac{1}{3}\left(\sqrt{10^{4024}-1\right)^{\frac{1}{2}}

    BTW
    When writing an exponent with ore than one character in LaTeX use {} on the exponent.
    [tex]10^{4024}[/tex] gives  10^{4024} .
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2013
    From
    Japan
    Posts
    4

    Re: Find the 2013th digit after the decimal point in the expression of...

    Can you show me more detail?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,969
    Thanks
    1788
    Awards
    1

    Re: Find the 2013th digit after the decimal point in the expression of...

    Quote Originally Posted by coriander View Post
    Can you show me more detail?

    No, I am not going to do that. It is too darn messy.
    You can look up binomial series.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,453
    Thanks
    1868

    Re: Find the 2013th digit after the decimal point in the expression of...

    You might want to specifically look up the generalised binomial series since this has a fractional exponent. It's about 2/3 of the way down this page:
    Binomial theorem - Wikipedia, the free encyclopedia
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: August 20th 2011, 01:09 AM
  2. Leading digit in decimal notation
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: January 17th 2011, 03:50 PM
  3. Binary Digit & Decimal value
    Posted in the Algebra Forum
    Replies: 5
    Last Post: February 22nd 2010, 08:22 PM
  4. last decimal digit
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 12th 2008, 12:16 AM
  5. decimal digit as final digit
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: February 25th 2008, 08:18 PM

Search Tags


/mathhelpforum @mathhelpforum