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Math Help - prove this convergence

  1. #1
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    prove this convergence

    suppose that:

    sigma ( An ) converges and An >0
    Show that there exist Bn with Bn/An tends to 0 and Sigma( Bn) converges
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  2. #2
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    Quote Originally Posted by szpengchao View Post
    suppose that:

    sigma ( An ) converges and An >0
    Show that there exist Bn with Bn/An tends to 0 and Sigma( Bn) converges
    If \sum_{n=0}^{\infty}a_n converges then it absolutely converges, which means \sum_{n=0}^{\infty}a_n^2 will converge. Take b_n = a_n^2.
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