Fibonacci Partial Sums Tricks
The paper discusses a mathematical trick for summing Fibonacci-like sequences, identifies the largest Fibonacci divisor of sums, and generalizes the method for Pell-like sequences, excluding Jacobsthal-like sequences.
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The paper titled "Fibonacci Partial Sums Tricks" explores a mathematical trick involving Fibonacci-like sequences. The authors demonstrate that a magician can quickly calculate the sum of the first ten terms of such a sequence by multiplying the seventh term by 11. This method is rooted in the divisibility properties of the partial sums of Fibonacci-like sequences. The research also identifies the largest Fibonacci number that divides the sum of Fibonacci numbers from 1 to n and extends the trick to other second-order recurrences. Additionally, the authors discuss the applicability of this trick to Pell-like sequences while noting that it does not apply to Jacobsthal-like sequences. The paper consists of 26 pages and includes 9 tables, contributing to the fields of history and overview in mathematics as well as number theory.
- The paper presents a mathematical trick for quickly summing Fibonacci-like sequences.
- It identifies the largest Fibonacci number that divides the sum of Fibonacci numbers from 1 to n.
- The trick is generalized for other second-order recurrences, including Pell-like sequences.
- The authors note that the trick does not apply to Jacobsthal-like sequences.
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