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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Originally Posted by paupsers 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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