Closed forms for certain fibonacci type sums that involve second order products

Publication Type:
Journal Article
Citation:
Fibonacci Quarterly, 2017, 55 (3), pp. 195 - 200
Issue Date:
2017-08-01
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In this paper, we present closed forms for certain finite sums in which the summand is a product of generalized Fibonacci numbers. We present our results in the form of six theorems that feature a generalized Fibonacci sequence {Wn}, and an accompanying sequence {Wn}- We add a further layer of generalization to our results with the use of three parameters s, k, and m. The inspiration for this paper comes from a website of Knott that lists so-called order 2 summations involving the Fibonacci and Lucas numbers. Probably the most well-known of these summations is σni=1Fi2=FnFn+1.
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