Answer to Question #2334 in Real Analysis for Joanna
or give a counterexample.
∑(a(n)+b(n)) = A + B
∑( (a(n)+a(n+1))/2) =& 0.5(∑(a(n) + ∑(a(n+1))) = 0.5∑(a(n))+0.5 ∑ (a(n+1)) .
Whereas the ∑(a(n)) converges absolutely (a(n)>0) , then ∑( (a(n)+a(n+1)/2)& converges too because at in right part of the equation there are two convergent series.
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