On the Sum of Reciprocal Tribonacci Numbers

Takao Komatsu1
1 Graduate School of Science and Technology Hirosaki University, Hirosaki, 036-8561, Japan

Abstract

The Tribonacci Zeta functions are defined by \(\zeta_T(s) = \sum_{k=1}^{\infty} {T_{k}^{-s}}\). We discuss the partial infinite sum \(\sum_{n=1}^{\infty} {T_{k}^{-s}}\) for some positive integer \(n\). We also consider the continued fraction expansion including Tribonacci numbers.