Abstract
Given a set of sequences defined by linear recurrence relations 1 method is described for finding the indefinite (and definite) sums of problems of terms from the sequences: for example, Σ1≈k≈nFk3=FnFn+1 when {Fk} is the sequence of Fibonacci numbers. The method is applicable when the subscripts of the factors in the product are linear functions of k (the summation variable). The sums found are expressed as a linear combination of terms, where each term is a product of factors, and each factor is a term from one of the original sequences. The results generalize many summations found in the literature and provide a vehicle for mechanically determining solutions in other cases.
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