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Math Help - diverging sequences - sum/product converging

  1. #1
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    diverging sequences - sum/product converging

    hello,

    I am supposed to find two diverging sequences whose sum and products converge, and whose elements are all >= 0. Anyone who could give me a hint? (-1)^n and (-1)^(n+1) works execpt for that fact that not all elements are >= 0.

    thank you -
    oz.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by ozfingwe View Post
    hello,

    I am supposed to find two diverging sequences whose sum and products converge, and whose elements are all >= 0. Anyone who could give me a hint? (-1)^n and (-1)^(n+1) works execpt for that fact that not all elements are >= 0.

    thank you -
    oz.
    I am not sure if this is what you mean. You should be more specific.

    a_n=-n,\tilde{a}_n=n+1,a_n+\tilde{a}_n=1

    b_n=(-1)^n,\tilde{b}_n=(-1)^n
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  3. #3
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    I'm sorry for the confusion, the sequences must hold to this:

    an >= 0 and bn >= 0 for all n...

    oz.
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