Geodesic
Reciprocal series of squares of Fibonacci related sequences with subscripts in arithmetic progression
Journal of integer sequences, Tome 18 (2015) no. 8.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {18},
     number = {8},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_8_a0/}
}
TY  - JOUR
AU  - Melham, R.S.
TI  - Reciprocal series of squares of Fibonacci related sequences with subscripts in arithmetic progression
JO  - Journal of integer sequences
PY  - 2015
VL  - 18
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JIS_2015__18_8_a0/
LA  - en
ID  - JIS_2015__18_8_a0
ER  - 
%0 Journal Article
%A Melham, R.S.
%T Reciprocal series of squares of Fibonacci related sequences with subscripts in arithmetic progression
%J Journal of integer sequences
%D 2015
%V 18
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JIS_2015__18_8_a0/
%G en
%F JIS_2015__18_8_a0
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/