Corpus ID: 11621528

Reciprocal Series of Squares of Fibonacci Related Sequences with Subscripts in Arithmetic Progression

@article{Melham2015ReciprocalSO,
  title={Reciprocal Series of Squares of Fibonacci Related Sequences with Subscripts in Arithmetic Progression},
  author={R. Melham},
  journal={J. Integer Seq.},
  year={2015},
  volume={18},
  pages={15.8.7}
}
  • R. Melham
  • Published 2015
  • Mathematics, Computer Science
  • J. Integer Seq.
In this paper, we derive closed forms for reciprocal series, both finite and infinite, that involve Fibonacci numbers. The term that defines the denominator of each summand generates squares of Fibonacci related numbers with subscripts in arithmetic progression. Our method employs certain algebraic identities that we believe are new. These identities exhibit the telescoping effect when summed. 
2 Citations
New results on reciprocal series related to Fibonacci and Lucas numbers with subscripts in arithmetic progression
  • 2
  • PDF
On two new classes of Fibonacci and Lucas reciprocal sums with subscripts in arithmetic progression
  • Highly Influenced
  • PDF

References

SHOWING 1-10 OF 12 REFERENCES
On reciprocal series related to Fibonacci numbers with subscripts in arithmetic progression
  • Fibonacci Quart
  • 1981
A solution to a tantalizing problem, Fibonacci Quart
  • 1986
Published in Journal of Integer Sequences
  • Published in Journal of Integer Sequences
  • 2015
Mathematics Subject Classification: Primary 11B39; Secondary 11B37. Keywords: reciprocal summation, Fibonacci number, Lucas number
  • Mathematics Subject Classification: Primary 11B39; Secondary 11B37. Keywords: reciprocal summation, Fibonacci number, Lucas number
  • 2010
Summation of certain reciprocal series related to Fibonacci and Lucas numbers, Fibonacci Quart
  • Summation of certain reciprocal series related to Fibonacci and Lucas numbers, Fibonacci Quart
  • 1991
Summation of reciprocal series of numerical functions of second order, Fibonacci Quart
  • Summation of reciprocal series of numerical functions of second order, Fibonacci Quart
  • 1986
On certain series of reciprocals of Fibonacci numbers, Fibonacci Quart
  • On certain series of reciprocals of Fibonacci numbers, Fibonacci Quart
  • 1984
On reciprocal series related to Fibonacci numbers with subscripts in arithmetic progression, Fibonacci Quart
  • On reciprocal series related to Fibonacci numbers with subscripts in arithmetic progression, Fibonacci Quart
  • 1981
...
1
2
...