Results 1 to 4 of 4

Math Help - Proof of Limit Properties

  1. #1
    Member
    Joined
    Oct 2008
    Posts
    82

    Proof of Limit Properties

    Let {xn} as n tends to infinity be a sequence convergent to 0. Let {yn} as n tends to infinity be a bounded sequence. Show that:

    lim as n tends to infinity(xnyn
    )=0

    And is is this true for all sequences of {yn
    } as n tends to infinity or only those that are bounded? Can you provide a proof or counterexample for this
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by amm345 View Post
    Let {xn} as n tends to infinity be a sequence convergent to 0. Let {yn} as n tends to infinity be a bounded sequence. Show that:

    lim as n tends to infinity(xnyn
    )=0

    And is is this true for all sequences of {yn} as n tends to infinity or only those that are bounded? Can you provide a proof or counterexample for this
    Here is a hint to get you started:

    Since y_n is bounded it is always less than some number lets call it M. i.e |y_n|<M for all n

    Now try to show that |x_ny_n-0|< \epsilon
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2008
    Posts
    82
    I got that part, now I just need to figure out what happens when yn is unbounded.
    Any hints?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by amm345 View Post
    I got that part, now I just need to figure out what happens when yn is unbounded.
    Any hints?
    The bounded part is needed.

    x_n=\frac{1}{n}, y_n=n^2

    x_ny_n=n this is unbounded
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find the limit of the function with the given properties
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: November 23rd 2011, 11:25 AM
  2. Permutation matrix properties proof
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: April 6th 2011, 03:17 AM
  3. Sequences / Limit properties
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 14th 2010, 06:15 PM
  4. some help with limit properties...
    Posted in the Calculus Forum
    Replies: 12
    Last Post: October 8th 2009, 08:32 PM
  5. Properties of Transpose Proof!
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: February 1st 2009, 05:53 PM

Search Tags


/mathhelpforum @mathhelpforum