values of FnFn-1 for 1<n<26


The golden ratioMathworldPlanetmath ϕ is an irrational number, approximately 1.6180339887498948482045868. Dividing one Fibonacci numberDlmfMathworldPlanetmath by the previous gives better and better approximations to the golden ratio the bigger the numbers get. One division gets a little under, then the next a little over, as the table below shows. 144 divided by 89 is probably good enough for most practical purposes.

Fn Fn-1 FnFn-1 to 20 decimal places Approximation error
1 1 1.00000000000000000000 -0.61803398874989484820
2 1 2.00000000000000000000 0.38196601125010515179
3 2 1.50000000000000000000 -0.11803398874989484820
5 3 1.66666666666666666666 0.04863267791677181846
8 5 1.60000000000000000000 -0.01803398874989484820
13 8 1.62500000000000000000 0.00696601125010515179
21 13 1.61538461538461538461 -0.00264937336527946358
34 21 1.61904761904761904761 0.00101363029772419941
55 34 1.61764705882352941176 -0.00038692992636543643
89 55 1.61818181818181818181 0.00014782943192333361
144 89 1.61797752808988764044 -0.00005646066000720775
233 144 1.61805555555555555555 0.00002156680566070735
377 233 1.61802575107296137339 -0.00000823767693347481
610 377 1.61803713527851458885 0.00000314652861974065
987 610 1.61803278688524590163 -1.20186464894656524257
1597 987 1.61803444782168186423 0.00000045907178701603
2584 1597 1.61803381340012523481 -0.00000017534976961338
4181 2584 1.61803405572755417956 0.00000066977659331361
6765 4181 1.61803396316670652953 -0.00000002558318831866
10946 6765 1.61803399852180339985 0.00000000977190855164
17711 10946 1.61803398501735793897 -0.00000000373253690923
28657 17711 1.61803399017559708655 0.00000000142570223835
46368 28657 1.61803398820532505147 -0.00000000054456979673
75025 46368 1.61803398895790200138 0.00000000020800715317
Title values of FnFn-1 for 1<n<26
Canonical name ValuesOffracFnFn1For1N26
Date of creation 2013-03-22 17:23:54
Last modified on 2013-03-22 17:23:54
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 4
Author PrimeFan (13766)
Entry type Example
Classification msc 40A05
Classification msc 11B39