Results 1 to 13 of 13

Math Help - Hard inequality,Please help me

  1. #1
    Newbie
    Joined
    Apr 2008
    Posts
    2

    Hard inequality,Please help me

    If $n\in N$, $n>1$ and $\alpha \in [0,1]$ prove that
    $$(n^\alpha-(n-1)^\alpha)(2^\alpha+n-n^\alpha-(n-1)^\alpha-1)+(n-1)^\alpha \geq 1$$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641

    ?????????

    Quote Originally Posted by uyanga View Post
    If $n\in N$, $n>1$ and $\alpha \in [0,1]$ prove that
    $$(n^\alpha-(n-1)^\alpha)(2^\alpha+n-n^\alpha-(n-1)^\alpha-1)+(n-1)^\alpha \geq 1$$
    With all these $ I can't discern what the problem is
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member angel.white's Avatar
    Joined
    Oct 2007
    Posts
    723
    Awards
    1
    TRANSLATION:

    If n\in N, n>1 and \alpha \in [0,1] prove that
    (n^\alpha-(n-1)^\alpha)(2^\alpha+n-n^\alpha-(n-1)^\alpha-1)+(n-1)^\alpha \geq 1
    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
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member angel.white's Avatar
    Joined
    Oct 2007
    Posts
    723
    Awards
    1
    Quote Originally Posted by angel.white View Post
    TRANSLATION:

    If n\in N, n>1 and \alpha \in [0,1] prove that
    (n^\alpha-(n-1)^\alpha)(2^\alpha+n-n^\alpha-(n-1)^\alpha-1)+(n-1)^\alpha \geq 1
    EDIT: This is wrong, I misread my own translation as \alpha \in \{0,1\}, this problem remains unsolved

    Case 1. \alpha = 0
    (n^0-(n-1)^0)(2^0+n-n^0-(n-1)^0-1)+(n-1)^0 \geq 1

    (1-1)(1+n-1-1-1)+1 \geq 1

    1 \geq 1

    TRUE


    Case 2. \alpha = 1
    (n^1-(n-1)^1)(2^1+n-n^1-(n-1)^1-1)+(n-1)^1 \geq 1

    (n-(n-1))(2+n-n-(n-1)-1)+(n-1) \geq 1

    (n-n+1)(2+n-n-n+1-1)+n-1 \geq 1

    (1)(2-n)+n-1 \geq 1

    2-n+n-1 \geq 1

    1 \geq 1

    TRUE

    Because Every value of alpha leads this to be true regardless of the value of n, this statement is always true.


    Edit:
    *sigh* stupid double posts >.<
    Last edited by angel.white; April 13th 2008 at 04:20 AM.
    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
    Hm, but nothing tells us that \alpha is an integer ?

    If you can prove that the function is increasing or decreasing, ok
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member angel.white's Avatar
    Joined
    Oct 2007
    Posts
    723
    Awards
    1
    Quote Originally Posted by Moo View Post
    Hm, but nothing tells us that \alpha is an integer ?

    If you can prove that the function is increasing or decreasing, ok
    not the best morning for me, I read it as being an element of a set containing the integers 0 and 1.

    Added a note stating it is not solved.
    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
    Listen to the unicorn, she does know all

    Now the problem is... understand what she says ^^
    Follow Math Help Forum on Facebook and Google+

  9. #9
    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
    Actually, your resolution can be used wisely...if the derivative (to \alpha) of the left member is more simple to study than the function itself... dunno, i didn't manage to solve it this morning :'(
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Super Member angel.white's Avatar
    Joined
    Oct 2007
    Posts
    723
    Awards
    1
    I must be overthinking this, because the solution I was working on just now was much more complicated than a post in "Elementary and Middle School Math Help" should warrant :/
    Follow Math Help Forum on Facebook and Google+

  11. #11
    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
    Didn't notice the category :/
    Perhaps the student went into the wrong one ?
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Newbie
    Joined
    Apr 2008
    Posts
    2

    I solved it

    I solved it.Now it is't hard inequality.
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Super Member angel.white's Avatar
    Joined
    Oct 2007
    Posts
    723
    Awards
    1
    Quote Originally Posted by uyanga View Post
    I solved it.Now it is't hard inequality.
    Post it, please, I'm really curious now.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: December 12th 2010, 01:16 PM
  2. Very hard inequality
    Posted in the Calculus Forum
    Replies: 5
    Last Post: February 10th 2010, 11:12 AM
  3. Hard/beautiful inequality --help!!
    Posted in the Algebra Forum
    Replies: 4
    Last Post: July 30th 2008, 11:37 PM
  4. Replies: 21
    Last Post: November 11th 2007, 07:20 AM
  5. ~~~inequality-- hard
    Posted in the Algebra Forum
    Replies: 1
    Last Post: August 7th 2006, 11:56 PM

Search Tags


/mathhelpforum @mathhelpforum