A324008 Decimal expansion of the sum of reciprocals of the products of k consecutive Fibonacci numbers, k>0.

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, 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, 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

Offset: 1

Author

Robert G. Wilson v, Feb 11 2019

Keywords

• nonn
• cons

Comments

Start of Array, the decimal expansion of Sum_{k>=1} 1/Product of the k consecutive Fibonacci numbers.

k A_xxxxx Expansion

1 A079586 3.3598856662431775531720113029189271796889051337319684864955538153251

2 A290565 1.7738775832851323438023627656769659228307232393594341108392290498649

3 A324007 0.7108553514293284168876944903842708330451180484103086399749735149369

4 0.2049150281252628794885329140859047056992270504855928446613784432368

5 0.0378540002823260756631035758318263246518410219564654534474085675610

6 0.0045033916811269635259578369635768898174496948588364334148979517071

7 0.0003362411268453457928115656517725694972839133469989715601437444837

8 0.0000157197618585596646075219438686990100758465336322798458353726393

9 A322711 0.0000004571522762064818372598445572889518549113726012557938158960751

...

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Total 6.0922434474344421121173873763040413146275243072847552367885514290335

Examples

			6.0922434474344421121173873763040413146275243072847552367885514290335796552...
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000045, A079586, A290565, A322711, A324007.

Programs

Mathematica

f[n_] := Sum[ N[ 1/Product[ Fibonacci@j, {j, k, k +n -1}], 110], {k, 525}]; Sum[ f[n], {n, 35}]