Suppose I have two conditionally convergent series $\sum \limits_{n=1}^{\infty} s_n$ and $\sum \limits_{n=1}^{\infty} t_n$.
According to http://mathworld.wolfram.com/ConvergentSeries.html the series $\sum \limits_{n=1}^{\infty} s_n + t_n$ will then also be convergent. Does this hold for conditionally convergent series? (I just want to be sure :D) Also, if it holds, can one say anything about the value of $\sum \limits_{n=1}^{\infty} s_n + t_n$?
Thanks
[Math] Sum of two conditionally convergent series
sequences-and-series
Related Question
- How to say about the terms of the sequence of partial sums $\{S_k \}$ of the conditionally convergent series $\sum\limits_{n=1}^{\infty} a_n$
- If $\sum\limits_{n=0}^{\infty} a_n\ $ is a conditionally convergent series, then is $\sum\limits_{n=0}^{\infty} |a_n+a_{n+1}|\ $ convergent
- Combining terms in a conditionally convergent series
Best Answer
This is a special case of the general property of sequences that the sum of two convergent series converges to the sum of their limits.