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Math Help - summation convergence

  1. #1
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    summation convergence

    Let \sum a_{k} from k=1 to infinity be a series of real numbers. Suppose that \sum a_{k} b_{k} from k=1 to infinity converges for every bounded sequence b_{k}. Prove that \sum a_{k} from k=1 to infinity converges absolutely.
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  2. #2
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    Pick b_k such that a_k b_k=|a_k| for each k. Verify that b_k is bounded (it should be bdd by 1, as you only need to use 1,-1).
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