4
$\begingroup$

Suppose $\sum a_n$ is convergent. Is $\sum {{a_n} \over {1+|a_n|}}$ convergent or divergent?

  • 2
    First consider the simple case that all $a_n\ge0$ and compare $a_n$ with $\frac{a_n}{1+|a_n|}$.2012-09-10
  • 0
    What about the case that part of $a_n$ are positive and part of it are negative2012-09-10

2 Answers 2