Sums of Certain Products of Fibonacci and Lucas Numbers - Part III

For the Fibonacci numbers, the summation formula ∑nk=1 F2k = FnFn+1 is well-known. Its charm lies in the fact that the right side is a product of terms from the Fibonacci sequence. In the earlier paper [5], the author presents similar formulas where, in each case, the right side consists of arbitrarily long products of an even number of distinct terms from the Fibonacci sequence. The formulas in question contain several parameters, and this contributes to their generality.In this paper, we provide additional results of a similar nature where the right side consists of arbitrarily long products of an odd number of distinct terms from the Fibonacci sequence. Most of the results that we present apply to a sequence that generalizes both the Fibonacci and Lucas numbers.