Calculus

For each sequence an find a number k such that nkan
has a finite non-zero limit.
(This is of use, because by the limit comparison test the series ∑n=1∞an and ∑n=1∞n−k both converge or both diverge.)

D. a_n = ( (7n^2+7n+7)/(5n^8+3n+5√n) )^7

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  1. not sure just what you mean by

    such that nkan has a finite non-zero limit.

    Nowhere in your expression is there a place for k, and the series clearly converges, so maybe you can 'splain a bit.

    Do you mean


    ∑an-k ??
    n=1

    Do you mean n^k an ??

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  2. ∞ ∞
    ∑a_n and ∑n^-k are the series that converge.
    n=1 n=1

    I have to find k from the a_n given, and am not sure how to do so.

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  3. Hmmm. I'm not sure just what you are after, either.
    However, as n->∞
    (7n^2+7n+7)/(5n^8+3n+5√n) -> 7n^2/5n^8 -> n^-6
    because all the lower powers of n don't really matter. (nor does the pesky 7/5)
    Maybe that will help some.

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