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Math Help - A proof of convergence of an infinite series

  1. #1
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    A proof of convergence of an infinite series

    Show that if \sum a_k is absolutely convergent and abs(b_k) \leq abs(a_k) fopr all k, then \sum b_k is absolutely convergent

    Here is what I have for this:
    Because abs(b_k) \leq abs(a_k), then \sum abs(b_k) \leq \sum abs(a_k)
    With the basic comparison test, since \sum abs(a_k) is convergent, then \sum abs(b_k) is convergent
    Since \sum abs(b_k) is convergent, by theorem \sum bk converges and is absolutely convergent.

    Is this proof sufficient?
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  2. #2
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    Yes that is a proof.
    You may want to add that {\color{blue}{0 \leqslant}} \sum {\left| {b_n } \right|} , just to be complete.
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