Geodesic
Reciprocal series of squares of Fibonacci related sequences with subscripts in arithmetic progression
Journal of integer sequences, Tome 18 (2015) no. 8
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.
Classification : 11B39, 11B37
Keywords: reciprocal summation, Fibonacci number, Lucas number 
@article{JIS_2015__18_8_a0,
     author = {Melham,  R.S.},
     title = {Reciprocal series of squares of {Fibonacci} related sequences with subscripts in arithmetic progression},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {8},
     zbl = {1332.11020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_8_a0/}
}
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Melham,  R.S. Reciprocal series of squares of Fibonacci related sequences with subscripts in arithmetic progression. Journal of integer sequences, Tome 18 (2015) no. 8. http://geodesic.mathdoc.fr/item/JIS_2015__18_8_a0/