This question seems trivial... Since addition is associative and commutative it shouldn't matter what order the terms are in...
Let sigma Un be a convergent series, and let sigma Vn be a rearrangement of it. In the rearrangement, suppose that no term of the original series is moved more than N places from its original position, where N is a fixed number. Show that the new series is convergent and has the same value as the old one.
Help please !