160225(3)

Ruby


隣り合う階乗の和(3)

e = 1 / 0! + 1 / 1! + 1 / 2! + …
1 = 1 / (0! + 1!) + 1 / (1! + 2!) + 1 / (2! + 3!) + …

? = 1 / (0! + 1! + 2!) + 1 / (1! + 2! + 3!) + 1 / (2! + 3! + 4!) + …

以下の計算により、
? はおよそ
0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422
くらいだとわかる。
（実際は、
0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077421…
である。）

require 'bigdecimal'

def f(n)
  return 1 if n == 0
  (1..n).inject(:*)
end

def g(n)
  f(n - 1) + f(n) + f(n + 1)
end

def h(n)
  (1..n).inject(0){|s, i| s += 1r / g(i)}
end

(1..100).each{|i| p BigDecimal(h(i), 100).to_s("F")}

出力結果
"0.25"
"0.3611111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111"
"0.3923611111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111"
"0.3990277777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778"
"0.4001851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851852"
"0.4003552532123960695389266817838246409674981103552532123960695389266817838246409674981103552532123961"
"0.400376954601284958427815570672713529856386999244142101284958427815570672713529856386999244142101285"
"0.4003794041407715349514291313233112174911116710058509000307942106883905825704767503709302651101592901"
"0.4003796521566445508244450043391842333641275440217239159038100837042635984434926233868032809831751631"
"0.400379674931288537589643890750191856492962794069095175396281697387998494299600600706901813202919504"
"0.4003796768449912614775529638444501359364274227189090103953018815933678848541763404678267593130507993"
"0.4003796769932285892020601755311490021224730959440694150428860163569898279632989367699102408837118572"
"0.4003796770038799958285234913368684359598207654912854475196894682171310305081295995144051849251411594"
"0.4003796770045937311101600075412858749451609853994065902087333918289558769008772268299337350215924904"
"0.4003796770046385387101511392784493581403902123746653114992007140423098362865826442813829325025360031"
"0.4003796770046411847875669938862264865597624573817394136100103183068123999781029642046980408197497376"
"0.4003796770046413323022994749783652963809813190343328579599377827420827010789612536448674208937610743"
"0.4003796770046413400902697086224671334971740697554409361690589328931381968515990385199879812887390233"
"0.4003796770046413404807498828371227950525831785068742717570440350048786182368660163449766649418761121"
"0.4003796770046413404993907790879716152724380112435461101906511529001759291992847764750632472859809976"
"0.4003796770046413405002400182663418972679913150903304367143309813084224285933371187495847537750047843"
"0.4003796770046413405002770181549305385935694768566319592669874793685170640876859650598618632484666182"
"0.4003796770046413405002785627367695057069873152068823937232970822310320626811605972961415815969089564"
"0.4003796770046413405002786246274922357979319186774732980882942531005144027987147808208787723982100198"
"0.4003796770046413405002786270117194119756217841341497844805602313915293474839632623730829602834918963"
"0.4003796770046413405002786271001549439973566729708418725354942122598270760220827670934829619850255341"
"0.400379677004641340500278627103317694333102588098488484201116605904498830540542790589419559377118255"
"0.4003796770046413405002786271034268939747648419171380171004801482754603250375028759560824515405656806"
"0.400379677004641340500278627103430538296139363959260408257954939510935666976865710551057193298877557"
"0.4003796770046413405002786271034306559856595142997071466426019419908211242141338777309157195316982785"
"0.4003796770046413405002786271034306596672880580652400019677206193795961868575262836117700178295414007"
"0.400379677004641340500278627103430659778961615599998307718866136890366815849701224327490116216845271"
"0.400379677004641340500278627103430659782249150855062964805884883337415615994934748074230470540584834"
"0.4003796770046413405002786271034306597823431617580896746040937558394017239224026504477921736846353704"
"0.4003796770046413405002786271034306597823457753055707866116919282435169422913920336269772927467146621"
"0.400379677004641340500278627103430659782345845996534691884818240075630754730215162930957756365716118"
"0.4003796770046413405002786271034306597823458478581830757398295882000183318544985744425218771470029177"
"0.4003796770046413405002786271034306597823458479059507297776538572031921979342019212133642921728248012"
"0.4003796770046413405002786271034306597823458479071457067808040334063801494195181842139967150881911677"
"0.4003796770046413405002786271034306597823458479071748707888737154016073603650253765262804881272031445"
"0.4003796770046413405002786271034306597823458479071755655833403414706829972924544806968721692847793794"
"0.4003796770046413405002786271034306597823458479071755817505162589525894915548769495298197576392223146"
"0.4003796770046413405002786271034306597823458479071755821181509041639241667306347607369247371117154889"
"0.4003796770046413405002786271034306597823458479071755821263247849922806861809967144836597958571504218"
"0.4003796770046413405002786271034306597823458479071755821265025658467812656607933178125945193272430681"
"0.40037967700464134050027862710343065978234584790717558212650635020660343985906553362310732929517945"
"0.4003796770046413405002786271034306597823458479071755821265064290831399659649304125173312007967190358"
"0.4003796770046413405002786271034306597823458479071755821265064306935641700301506902471095006180660562"
"0.4003796770046413405002786271034306597823458479071755821265064307257860743131556393040194814336581745"
"0.4003796770046413405002786271034306597823458479071755821265064307264181291798671268217110674958397553"
"0.4003796770046413405002786271034306597823458479071755821265064307264302887561120719329057111004827605"
"0.4003796770046413405002786271034306597823458479071755821265064307264305182669572288276255563898325024"
"0.400379677004641340500278627103430659782345847907175582126506430726430522518671669352826490529181607"
"0.4003796770046413405002786271034306597823458479071755821265064307264305225960020876192945143804234095"
"0.4003796770046413405002786271034306597823458479071755821265064307264305225973834445924147062511126955"
"0.4003796770046413405002786271034306597823458479071755821265064307264305225974076866555261806723694828"
"0.4003796770046413405002786271034306597823458479071755821265064307264305225974081047508158506039701671"
"0.400379677004641340500278627103430659782345847907175582126506430726430522597408111839283847044042866"
"0.4003796770046413405002786271034306597823458479071755821265064307264305225974081119574589289195595952"
"0.4003796770046413405002786271034306597823458479071755821265064307264305225974081119593967636311682854"
"0.4003796770046413405002786271034306597823458479071755821265064307264305225974081119594280274317314832"
"0.4003796770046413405002786271034306597823458479071755821265064307264305225974081119594285238116651698"
"0.4003796770046413405002786271034306597823458479071755821265064307264305225974081119594285315695562547"
"0.4003796770046413405002786271034306597823458479071755821265064307264305225974081119594285316889375711"
"0.4003796770046413405002786271034306597823458479071755821265064307264305225974081119594285316907468071"
"0.4003796770046413405002786271034306597823458479071755821265064307264305225974081119594285316907738168"
"0.4003796770046413405002786271034306597823458479071755821265064307264305225974081119594285316907742141"
"0.4003796770046413405002786271034306597823458479071755821265064307264305225974081119594285316907742199"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"
"0.40037967700464134050027862710343065978234584790717558212650643072643052259740811195942853169077422"