On sums and reciprocal sum of generalized fibonacci numbers

Abstract

The purpose of this report is to analyze the properties of Fibonacci numbers modulo a Lucas numbers. Any Fibonacci number, except the first two, is the sum of the two immediately preceding Fibonacci numbers and closely related to Fibonacci numbers are Lucas number. Fibonacci numbers are used in the application of computer algorithms. They can be used to compress audio files and generate code. The most recently Fibonacci number have been used to symbolize mathematical relationship in the Davinci code as well as in the TV shows fringe, criminal minds. In this report, some generalized identities of Holliday and Komatsu have been studied results of Liu and Zhao obtained by applying the floor function to the reciprocal of infinite sums of reciprocal generalized Fibonacci numbers and the infinite sums of reciprocal generalized Fibonacci sums have been extended.