Suppose $\sum a_n$ is convergent. Is $\sum {{a_n} \over {1+|a_n|}}$ convergent or divergent?
Convergent or divergent series examples
4
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calculus
sequences-and-series
analysis
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2First consider the simple case that all $a_n\ge0$ and compare $a_n$ with $\frac{a_n}{1+|a_n|}$. – 2012-09-10
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0What about the case that part of $a_n$ are positive and part of it are negative – 2012-09-10