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Math Help - Real Analysis Proof

  1. #1
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    Jul 2011
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    Real Analysis Proof

    I was having a problem with a hw question. Could some give me a detailed proof to answer.
    Prove that if the series ak converges and the series bk diverges then series ak+bk diverges.
    I know i need to prove by contradiction. thanks
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  2. #2
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    Aug 2009
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    Re: Real Analysis Proof

    Suppose c_k = (a_k + b_k) converges. Then by our limit laws c_k - a_k must converge as well. But c_k - a_k = (a_k + b_k) - a_k = b_k, and we know that b_k diverges. This is the contradiction we're looking for.
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