The Infinite Sum of Reciprocal of the Fibonacci Numbers
Received:October 13, 2010  Revised:January 12, 2011
Key Words: Fibonacci numbers   reciprocals   infinite sum   elementary method   identity.  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11071194).
Author NameAffiliation
Guo Jie ZHANG Department of Mathematics, Northwest University, Shaanxi 710127, P. R. China 
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Abstract:
      In this paper, we consider infinite sums of the reciprocals of the Fibonacci numbers. Then applying the floor function to the reciprocals of this sums, we obtain a new identity involving the Fibonacci numbers.
Citation:
DOI:10.3770/j.issn:1000-341X.2011.06.010
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