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  1. #1
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    Quick question

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

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

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

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


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