Is the order of terms in a series important?

The basic facts about rearranging terms

1. A convergent infinite series is either absolutely convergent or conditionally convergent but never both.
   
   
2. The order of the terms in an absolutely convergent series may be rearranged without affecting the sum of the series.
   
   
3. The order of the terms in a conditionally convergent series is always significant.
   
   
4. A power series (in particular any Taylor series) is absolutely convergent inside its disk of convergence.

Examples