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**wopashui** Suppose that $\displaystyle \displaystyle \sum a_n$ and $\displaystyle \displaystyle \sum b_n $are absolutely convergent series and $\displaystyle \displaystyle \sum c_n $ is conditionally convergent. For each of the series $\displaystyle \displaystyle \sum(a_n+b_n)$, $\displaystyle \displaystyle \sum(a_n+c_n) $and $\displaystyle \displaystyle \sum (a_nc_n)$, determine whether is it absolutely convergent or conditionally convergent or neither.

I have already given the answer which are absolutely,conditionally and absolutely, I just need some explaination for $\displaystyle \displaystyle \sum(a_n+c_n) $and $\displaystyle \displaystyle \sum (a_nc_n)$, why is conditionally and absolutely