A(n) = 2(n+1)/(3ⁿ-1)
这个数列迄今为止还没有找到求和公式。
如果要求和，只能通过手工计算，或者编程求解。
写了一段fortran代码，因为随着n的增大，分母增加很快，需要更多位小数才能观察到这些变化。因此，使用了大整数模块来计算出更多有效数字。输出的结果，小数点后65位。
下面是n=1到100的计算结果：
n = 1，S = 2.0000000000000000000000000000000000000000000000000000000000000000；
n = 2，S = 2.7500000000000000000000000000000000000000000000000000000000000000；
n = 3，S = 3.0576923076923076923076923076923076923076923076923076923076923076；
n = 4，S = 3.1826923076923076923076923076923076923076923076923076923076923076；
n = 5，S = 3.2322790845518118245390972663699936427209154481881754609027336300；
n = 6，S = 3.2515098537825810553083280356007628734901462174189446916719643992；
n = 7，S = 3.2588291584486377799194899752164993785221681753329428618457978850；
n = 8，S = 3.2615730608876621701633924142408896224246071997231867642848222752；
n = 9，S = 3.2625892177822867001908286503957519331653855759044691542858384321；
n = 10，S = 3.2629617960237174006379225401125924696780532361131129694870306825；
n = 11，S = 3.2630972774909816911101883547513650075846387644343846888597514891；
n = 12，S = 3.2631462011700423564722235798002886866453041264696097377834305497；
n = 13，S = 3.2631637634943407102552109562524733770654325572383001278050196641；
n = 14，S = 3.2631700357503959462509357865252245223793882433311194818128240233；
n = 15，S = 3.2631722658855714084081204527290452178386797042968544305259872428；
n = 16，S = 3.2631730557250760210708273906792537354678974472514860493810358969；
n = 17，S = 3.2631733344919556847342507027856765228266433655042446296281320714；
n = 18，S = 3.2631734325765980230093498761675447527794175719112119348781321695；
n = 19，S = 3.2631734669922619421295936854034951082048636393109892583052860385；
n = 20，S = 3.2631734790377443069124578051351309386278745946198405884879035814；
n = 21，S = 3.2631734832441032271434957168891933326674826655902150743187693144；
n = 22，S = 3.2631734847099555780396770935317637125044795323659954901525850939；
n = 23，S = 3.2631734852198172652970824715973220869822221754004655699020462193；
n = 24，S = 3.2631734853968525733713167900801011937972616220140841456357934278；
n = 25，S = 3.2631734854582248135035731531082776855946935294522910682456930968；
n = 26，S = 3.2631734854794690504724144094588941855294012507842353707768030390；
n = 27，S = 3.2631734854868127373258390905304191593570752077494039087012136085；
n = 28，S = 3.2631734854893480577871402468694034851321091873996337406781549403；
n = 29，S = 3.2631734854902223062220716546127320418118836491014911392657055914；
n = 30，S = 3.2631734854905234362385480254658513711645143477147379188193457103；
n = 31，S = 3.2631734854906270508678732280045432367923948134008881011566150985；
n = 32，S = 3.2631734854906626683967037663387758880263959717157528571260549771；
n = 33，S = 3.2631734854906749006793324360653236300745384177395963419246594217；
n = 34，S = 3.2631734854906790980312148227356944906350056036777574458923479751；
n = 35，S = 3.2631734854906805371232887838797641154383508431849226448141694062；
n = 36，S = 3.2631734854906810301455733816791147322278112409004908035536623038；
n = 37，S = 3.2631734854906811989279771178626754549711734498358754001407410625；
n = 38，S = 3.2631734854906812566693257644517882483156252621879818982885104942；
n = 39，S = 3.2631734854906812764099577803796900482637223284988536762933699529；
n = 40，S = 3.2631734854906812831546737191550564954697808644939997601050218662；
n = 41，S = 3.2631734854906812854577474543466450382919018432084266763007107818；
n = 42，S = 3.2631734854906812862437170623882189060660372092701804942497146753；
n = 43，S = 3.2631734854906812865117997193946472020493802424939563225872891798；
n = 44，S = 3.2631734854906812866031915342832023029526070298765771466116320134；
n = 45，S = 3.2631734854906812866343324489859692262233150757646407195492388703；
n = 46，S = 3.2631734854906812866449384126890854971923219444409303466670744928；
n = 47，S = 3.2631734854906812866485489535241889085860261387898442216725038208；
n = 48，S = 3.2631734854906812866497775403361338194074948963400798180520168153；
n = 49，S = 3.2631734854906812866501954270068633809113958307897514321545406310；
n = 50，S = 3.2631734854906812866503375084749114318227221481068134365829416294；
n = 51，S = 3.2631734854906812866503857976013068478187284781305143141075054347；
n = 52，S = 3.2631734854906812866504022035224540083814742184540009737798991339；
n = 53，S = 3.2631734854906812866504077753447304025348595642236668149459163956；
n = 54，S = 3.2631734854906812866504096670127872030190336013676241064638949463；
n = 55，S = 3.2631734854906812866504103090334610262136623654892022509184787159；
n = 56，S = 3.2631734854906812866504105268619039305118399818875940032015000468；
n = 57，S = 3.2631734854906812866504106007452354419112218634730133338361443595；
n = 58，S = 3.2631734854906812866504106257976294601443456049301382686435563253；
n = 59，S = 3.2631734854906812866504106342899664154776078901698416351728859660；
n = 60，S = 3.2631734854906812866504106371679250503405467757232966648053777083；
n = 61，S = 3.2631734854906812866504106381429711452121435566211885327529642968；
n = 62，S = 3.2631734854906812866504106384732286934751037566027325525399317094；
n = 63，S = 3.2631734854906812866504106385850619373313442476017739137374395435；
n = 64，S = 3.2631734854906812866504106386229221500951756638254077078928237892；
n = 65，S = 3.2631734854906812866504106386357363759537032200857145305300282767；
n = 66，S = 3.2631734854906812866504106386400725028856292113455153240486779995；
n = 67，S = 3.2631734854906812866504106386415394513004101437120150949903107098；
n = 68，S = 3.2631734854906812866504106386420356250289389884830370763382158877；
n = 69，S = 3.2631734854906812866504106386422034132463158925118850893544157059；
n = 70，S = 3.2631734854906812866504106386422601416436195124454479889932261206；
n = 71，S = 3.2631734854906812866504106386422793174398911586201734761950775284；
n = 72，S = 3.2631734854906812866504106386422857981488162982995945899253328653；
n = 73，S = 3.2631734854906812866504106386422879879774028751775725005008529334；
n = 74，S = 3.2631734854906812866504106386422887277843577997985109838033934970；
n = 75，S = 3.2631734854906812866504106386422889776747070187815835381633627540；
n = 76，S = 3.2631734854906812866504106386422890620675003953679720762586155294；
n = 77，S = 3.2631734854906812866504106386422890905637682887607785956154541289；
n = 78，S = 3.2631734854906812866504106386422891001843031758463842153983184424；
n = 79，S = 3.2631734854906812866504106386422891034317411124153650153250236959；
n = 80，S = 3.2631734854906812866504106386422891045277514160073960353002867190；
n = 81，S = 3.2631734854906812866504106386422891048975985143388632930697170395；
n = 82，S = 3.2631734854906812866504106386422891050223843239385046849187524729；
n = 83，S = 3.2631734854906812866504106386422891050644807416347692508437282817；
n = 84，S = 3.2631734854906812866504106386422891050786799301434299179215971061；
n = 85，S = 3.2631734854906812866504106386422891050834686760718409664262901214；
n = 86，S = 3.2631734854906812866504106386422891050850834857453749246429889289；
n = 87，S = 3.2631734854906812866504106386422891050856279426467963358424889100；
n = 88，S = 3.2631734854906812866504106386422891050858114906173512812847445854；
n = 89，S = 3.2631734854906812866504106386422891050858733607197855325574150378；
n = 90，S = 3.2631734854906812866504106386422891050858942132357911505789447088；
n = 91，S = 3.2631734854906812866504106386422891050859012404573022013407788836；
n = 92，S = 3.2631734854906812866504106386422891050859036083254200554018317034；
n = 93，S = 3.2631734854906812866504106386422891050859044061017751746912186750；
n = 94，S = 3.2631734854906812866504106386422891050859046748562210482106930093；
n = 95，S = 3.2631734854906812866504106386422891050859047653840343950804106799；
n = 96，S = 3.2631734854906812866504106386422891050859047958743048626025030897；
n = 97，S = 3.2631734854906812866504106386422891050859048061425059135205960662；
n = 98，S = 3.2631734854906812866504106386422891050859048096001654510746477828；
n = 99，S = 3.2631734854906812866504106386422891050859048107643605815642274854；
n = 100，S = 3.2631734854906812866504106386422891050859048111563062754957193186；
附：fortran代码
