Question concerning Infinite Series
Problem : The collection $\sum_{n=1}^{\infty} a_n$ deviate and also favorable. What can be claimed on the collection $\sum_{n=1}^{\infty} \frac{a_n}{1+n^{2}a_n}$?
Strategy :

First, I attempted dividing it right into 2 instances : $a_n \to \infty$, $a_n \to A$ (where $A$ is some const value).

Attempted the proportion examination and also obtained no place with that said.
I assume that the appropriate strategy is to examine each instance independently, yet my suspicion informs me that there is a workaround.
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Ma.H 20191202 02:54:35
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Answers: 2
Hint : Rewrite as $$\sum_{n=1}^{\infty} \frac{1}{\frac{1}{a_n} + n^2}.$$
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Mike Spivey 20191203 04:26:47
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