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Math Help - Quick question

  1. #1
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    Quick question

    We have \sum_1^\infty (-1)^ka_k.

    If \lim_{k->\infty} a_k>1 does \sum_1^\infty (-1)^ka_k diverge by the Divergence Theorem?
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  2. #2
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    Quote Originally Posted by paupsers View Post
    We have \sum_1^\infty (-1)^ka_k.

    If \lim_{k->\infty} a_k>1 does \sum_1^\infty (-1)^ka_k diverge by the Divergence Theorem?
    Yes. It diverges.

    If \lim_{n\to\infty} |a_k| \neq 0, then \lim_<br />
{n\to\infty} (-1)^k a_k does not exist.

    Thus \sum_{n \geq 1} (-1)^k a_k diverges.
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