包含广义Fibonacci数列倒数积的恒等式

Several identities relating to reciprocal products of generalized Fibonacci numbers

近年来众多学者研究了关于整数序列的倒数和取整问题,该文主要研究F_k^t-1/F_k^t及k^t-1/k^t的无穷乘积的取整问题,其中t和k为正整数,F_k为广义Fibonacci数列,建立了一些包含广义Fibonacci数列及正整数序列倒数积的恒等式。

This paper is inspired by the researches relating to reciprocal sums of some integer sequences. For positive integers t and k,the infinity products of Fk^t- 1/Fk^t and k^t-1/k^t are studied,where Fk denotes the generalized Fibonacci numbers. Then several new inequalities are established to obtain the identities related to the reciprocal products of generalized Fibonacci numbers and positive integer sequences.