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Answer by hamam_Abdallah for Inconclusive convergence tests and Divergence Test
You know that for a real or complex sequence $ ( u_n)$, we have the equivalence$$\boxed{\lim_{n\to+\infty}u_n=0\iff \lim_{n\to+\infty}|u_n|=0}$$So,$$\lim_{n\to+\infty}|u_n|\ne...
View ArticleAnswer by José Carlos Santos for Inconclusive convergence tests and...
Since the limit $\lim_{n\to\infty}(-1^n)\frac n{n+5}$ does not exist, then, in particular, you don't have $\lim_{n\to\infty}(-1^n)\frac n{n+5}=0$, and therefore the series diverges.
View ArticleInconclusive convergence tests and Divergence Test
What happens when the series is alternating and the tests that I know are inconclusive?$\sum_{n=1}^\infty (-1)^n (n/(n+5))$.The $b_n$ series is not decreasing, so I can't use the alternating series...
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