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Math Help - Questions on Series

  1. #1
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    Questions on Series

    An is a sequence and Sk is a sequence of partial sums of the series nΣ1 to infinity of An

    Does An Converge if An is less than 0 for all n and Sk greater than -6473 for all K

    I would like to say divergent because greater than - 6473 leads to infinity?? Obviously the series is all negative and so if its convergent it also absolutely convergent but we don't what An is so could it be not enough information has been provided??
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  2. #2
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    Quote Originally Posted by Some1Godlier View Post
    An is a sequence and Sk is a sequence of partial sums of the series nΣ1 to infinity of An

    Does An Converge if An is less than 0 for all n and Sk greater than -6473 for all K

    I would like to say divergent because greater than - 6473 leads to infinity?? Obviously the series is all negative and so if its convergent it also absolutely convergent but we don't what An is so could it be not enough information has been provided??
    Do you know that a decreasing bounded sequence conveges?
    Is the sequence \left(S_n\right) decreasing and bounded?
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  3. #3
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    Well yes, I know this is decreasing but is it bounded?? I thought decreasing only matter if we were talking positives??
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