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Maximum-likelihood sequence estimation (MLSE) of data sequences is considered as an approach to increasing data rates over band-limited channels, such as exist in analog telephone facilities. Analytical prediction of the efficacy of MLSE for specific channels had been viewed as intractable until Forney gave a formula for an asymptotic upper bound on the probability of symbol error . Forney's bound involved an infinite series, and letting the noise power No --} 0, he chose the asymptotically largest series term as an asymptotic bound on , ignoring a very basic perplexing open question: How do we know the bounding series is not identically infinity for all We show that under very general conditions Forney's bounding series converges for a nontrivial interval . As a corollary, we prove Forney's aforementioned asymptotic formula for . The analysis includes the class of channels with spectral nulls, since band edge nulls can be associated with telephone channels that are pulsed at high rates.