Zhang Fu-ling
Abstract
According to the definition and the recurrence property of generalized Fibonacci sequencesGn:Gn+1=uGn+vGn-1,G0=a,G1=b,where,some quadratic sum formulas of generalized Fibonacci numbers are proved,which are∑nk=1G2k、∑nk=1(-1)kG2k、∑nk=1kG2k、∑nk=1GkGk+1。
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According to the definition and the recurrence property of generalized Fibonacci sequencesGn:Gn+1=uGn+vGn-1,G0=a,G1=b,where,some quadratic sum formulas of generalized Fibonacci numbers are proved,which are∑nk=1G2k、∑nk=1(-1)kG2k、∑nk=1kG2k、∑nk=1GkGk+1。
Key concepts: Fibonacci number, Mathematics, Sequence (biology), Combinatorics, Statistics, Applied mathematics, Discrete mathematics, Chemistry