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Math Help - new convergence problem

  1. #1
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    new convergence problem

    let {a _{n}} and {b _{n}} be real sequences for every integer greater than or equal to 1. Suppose b _{n} does not equal 0 for all integer n greater than or equal to 1. if {b _{n}} and {a _{n}/b _{n}} both converge, prove that {a _{n}} also converges.

    So I am not sure what technique I am supposed to use in this problem. Can somebody help please? Thanks.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by janae77 View Post
    let {a _{n}} and {b _{n}} be real sequences for every integer greater than or equal to 1. Suppose b _{n} does not equal 0 for all integer n greater than or equal to 1. if {b _{n}} and {a _{n}/b _{n}} both converge, prove that {a _{n}} also converges.

    So I am not sure what technique I am supposed to use in this problem. Can somebody help please? Thanks.
    What are the properties of convergent sequences with relation to multiplication?
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  3. #3
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    If {bn} and {an/bn} both converge, that implies that an = (an/bn) * bn converges, since it is a product of two convergent sequences.
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