摘要：The Fibonacci sequence has been generalized in many ways. One of them is defined by the relation u n = a u n − 1 + u n − 2 if n is even, u n = b u n − 1 + u n − 2 if n is odd, with initial values u 0 = 0 and u 1 = 1 , where a and b are positive integers. In this paper, we consider the reciprocal sum of u n and then establish some identities relating to ∥ ( ∑ k = n ∞ 1 u k ) − 1 ∥ , where ∥ x ∥ denotes the nearest integer to x. MSC:11B39.
关键词：generalized Fibonacci sequence ; infinite sum ; reciprocal sum
