Abstract
A sequence s n ⊂ℂ is being elongated with respect to a sequence m n ⊂ℕ if the term s n is listed m n-times and the resulting modified sequence is considered instead of s n. As a main result it is shown that there exists an elongation of the partial sums of a power series which is Cesaro summable outside the circle of convergence if and only if the power series is overcon vergent.
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