The elementary renewal theorem does not follow trivially from the renewal law of large numbers, because the

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The elementary renewal theorem does not follow trivially from the renewal law of large numbers, because the convergence of a sequence of random variables \(X_{1}, X_{2}, X_{3}, \ldots\) to a constant does not necessarily imply

that their expectations converge to the same constant. Show this last statement by considering the sequence of random variables defined by

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