First consider 1. The second step is to consider the square root of two. Third, think about the cube root of three. Now we also want the fourth root of four, fifth root of five, and so on. Now after we get all of these we want to add them as an alternating = series. 1^(1/1)-2^(1/2)+3^(1/3)- 4^(1/4)+5^(1/5)... The sequence of incomplete sums has two limit points, which vary by one since lim(n^(1/n)) =3D 1 as n approaches infinity. Therefore, it = suffices us to focus on the case where the upper limit is even. This converges quite slowly. It is a challenge to compute! approx. 0.187859642462067120248517934054 5k digits at bottom. But here is a neat approximation! 4124*Pi/68966 = 0.1878596424818650830180080229 Closer: 4124.000000001487803363004788*Pi/68966.000007293 = 0.1878596424620671202485179339822595680712531722091448381989191587 Computed in September 1999 by Marvin Ray Burns on a Pentium II 350 MHz with 64 Mb of ram. 0.18785964246206712024851793405427323005590309490013878617200468408947723 1564660213703296654433107496903842345856258019061231370094759226630438929 3488961841208373366260816136027381263793734352832125527639621714893217020 7628206217151671540841268044836354167199851976802527598938993914457983505 5613509648521071207844423095868129497688526949564204255586483670441042527 9524710606660926339748341031157816786416689154600342222588380025455396892 9471142122189105098328712277308020036445215390536395055332203470627551159 8128280395102192649146731762935161906598160186642458249506972033819929584 2093551516251439935760076459329128145170908242491588320416906640933443591 4806705564692806787007028115009380606938139385953360657987405562062348704 3293607378195646031047639506648930613606455280675151935082808373767192968 6639810309494963749627738304984632456347931157530028921252329181619562697 3697074865765476071178017195787368300965902260668753656305516567361288150 2014387561366865522106743053705910397357561914890936907779832035511933624 0463725349410542836369971702441855165483727935882200813448096105880203064 7819619596953756287834812334976385863010140727252923014723333362509185840 2480370404888196767676011985811167916935279685204416002708613722868894510 1510291998853690572865928708687542549253379439534758970356331344038263888 7986656195980733514739902565778133172261076127975852722742777308985774922 3059709625725627188367557529788792536168767394035432145136277254922931312 6276435732144621618778637715420542312822344629539653290332217147982028075 9842210655648900485368587070832688748773776350476891609831855362816671591 0841219342016438600025850842655643500695483283012054619320515593504002350 8351261335921740897007329784277128967365161960225077117388084262325697885 4653786904622270856748747470930693573266685908561628237538655124329756474 6491461917957586934299620814987853666317019726453426046837801075905514867 8719039578315060452444190757044511382058533398469219482879476486575931785 9581652749297782209597744091137143421692962459317532453734012995939950049 1791298368084854714392584670423852860832005366451058667815119645967607919 6431734307671534498300497128869401656600427062111079053164721504556329943 8840052111523901687731154569610283692050368961088060316036603828965332393 8352415451013753416567347260746489112008809983815204669541502637703557328 3592996630642717305158972116351999161135954670315408725287243998197872502 7467973886388970568674353778579810585561924921857169491356734627040774914 4879968206548281746588064223634816078095077705793931349582980660282527212 8491688809230325290270059917755059615835919993190869393039736611646514858 2199729253371067687386862350479158797379682698478780822234106187896746674 5068006440406555387521328149498070020985813222062010901126590344971741080 1063247564712834609549284370065147450218226120415643930308859826426256828 1260924911367339672359337145342169025601400501694699838759073429203617293 0153140040593624640678140077947561307736973240992352946479458077816460769 6240864595666084141126399988575739429315226283898798436350719371486573491 9620254284435104114728419738149338070662225731910214815857450428867284772 5043438671844314912894863544892949214325966084714960007253406621538756134 1325254274130158182476636432111506809477451406309160928029719327606796946 8609263620817634422729775463267371611103022200194984554072338596799729567 4531849043382633293188816033005401369031610430997377786393439313562149654 9969937314205819065334661573835222280871390934331325238360305287172314811 1510297058562812995589918303810719663081327016704986176831683295290537987 6003066657020343588496034210481148868121608361194460557191397329297068323 2645094571537170202325175198220852151188427534658891812172660333192804801 1747590461318984497207220682489191539332580026246272161764244687477896097 6490607047960535174020522799202111287653983538174011795526700337583139607 8847726709215700142824833574188212706558826075722384346836425460624376294 9725572084429109010146920322976340088313403816403729113113149598830486629 4496453219311357495645391238545666288156609986032544783986287801475697722 8191151861520827628240145565179425383818619479339940149759987240427388505 6441143756079520211579102553987653665393231584920065329570705591855222675 4284573681267069956582467476211159956779887108994312910340144254976593713 5216907789286769520555697938362195599913809621446502826784457775198333561 8744957998843531990905504564240610916094297513674772622513506116867915294 5364371773991392212648377880620387276808838103226728493308593907877273472 8272526200188560744654953143832715829738195578665687162281676008390755269 4743377480542717093388979753170189068955143939404845538298301981692536597 9747677854686504585964023817593013999612266766811738967050203329234908051 3690067470281709256521198479569202858477768560978920686214307401593342577 7262910166752349405574100207286898501479277429106643136941528199585609819 7652321625531862376426059132066712394239831074800890067697570607132333012 49195951646813480370178134651913158679