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%I #9 Feb 20 2019 21:11:02
%S 6,0,9,2,2,4,3,4,4,7,4,3,4,4,4,2,1,1,2,1,1,7,3,8,7,3,7,6,3,0,4,0,4,1,
%T 3,1,4,6,2,7,5,2,4,3,0,7,2,8,4,7,5,5,2,3,6,7,8,8,5,5,1,4,2,9,0,3,3,5,
%U 7,9,6,5,5,2,8,6,4,6,8,1,7,4,4,5,6,8,0,7,9,1,6,7,7,3,6,1,4,5,1,4,4,7,4,6,5
%N Decimal expansion of the sum of reciprocals of the products of k consecutive Fibonacci numbers, k>0.
%C Start of Array, the decimal expansion of Sum_{k>=1} 1/Product of the k consecutive Fibonacci numbers.
%C k A_xxxxx Expansion
%C 1 A079586 3.3598856662431775531720113029189271796889051337319684864955538153251
%C 2 A290565 1.7738775832851323438023627656769659228307232393594341108392290498649
%C 3 A324007 0.7108553514293284168876944903842708330451180484103086399749735149369
%C 4 0.2049150281252628794885329140859047056992270504855928446613784432368
%C 5 0.0378540002823260756631035758318263246518410219564654534474085675610
%C 6 0.0045033916811269635259578369635768898174496948588364334148979517071
%C 7 0.0003362411268453457928115656517725694972839133469989715601437444837
%C 8 0.0000157197618585596646075219438686990100758465336322798458353726393
%C 9 A322711 0.0000004571522762064818372598445572889518549113726012557938158960751
%C ...
%C ---------------------------------------------------------------------
%C Total 6.0922434474344421121173873763040413146275243072847552367885514290335
%H Robert G. Wilson v, <a href="/A324008/b324008.txt">Table of n, a(n) for n = 1..1000</a>
%e 6.0922434474344421121173873763040413146275243072847552367885514290335796552...
%t f[n_] := Sum[ N[ 1/Product[ Fibonacci@j, {j, k, k +n -1}], 110], {k, 525}]; Sum[ f[n], {n, 35}]
%Y Cf. A000045, A079586, A290565, A322711, A324007.
%K nonn,cons
%O 1,1
%A _Robert G. Wilson v_, Feb 11 2019
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