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Math Help - true or false

  1. #1
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    true or false

    if neither sequence {Xn} and {Yn} converges then {XnYn} does not converge

    i think this is false but am failing to find a counter-example?
    and ideas??
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by crafty View Post
    if neither sequence {Xn} and {Yn} converges then {XnYn} does not converge

    i think this is false but am failing to find a counter-example?
    and ideas??
    how about x_n = \cos n and y_n = \frac 1{\cos n} ?
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  3. #3
    MHF Contributor matheagle's Avatar
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    or x_n=y_n=(-1)^n=-1,1,-1,1,.....
    so x_ny_n=1,1,1,1,.....
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by matheagle View Post
    or x_n=y_n=(-1)^n=-1,1,-1,1,.....
    so x_ny_n=1,1,1,1,.....
    this was the example i had way in the back of my mind. i was grasping for it, but came up with what i posted earlier.

    both work though
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  5. #5
    MHF Contributor matheagle's Avatar
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    Or, how about
    x_n=0,1,0,1,0,1...
    and
    y_n=1,0,1,0,1,0...
    so x_ny_n=0,0,0,0,0,0....
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