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myininaya
 5 years ago
Evaluate
lim (1^(1/n)+2^(1/n)+...+2007^(1/n)2006)^n
ninfnity
myininaya
 5 years ago
Evaluate lim (1^(1/n)+2^(1/n)+...+2007^(1/n)2006)^n ninfnity

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myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{n \rightarrow \infty}( \sqrt[n]{1}+\sqrt[n]{2}+...+\sqrt[n]{2007}2006)^n\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0no i wish it were that easy andras

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0there you go polpak :)

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0this was a question i did in my senior seminar class. its been a while since i looked at it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I misunderstood it :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this is not diverging??

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0i put it into maple and maple is still evaluating lol

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0wolfram alpha no result can be reached

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but the sum is surely bigger than 1 and if u take the nth power of it than it goes to infinity

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0you will get a big freaking number

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0than what am I misunderstanding? :)

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0the number does exist though

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0really??? I dont believe you

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if you take lim 1.001^n as n tends to infinity. this is diverging for sure

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0i will give you the answer it is 2007!

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0thats factorial not exclamation

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.02007? surprising :) but I start to understand why it converges

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah, I cannot imagine such a big number

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0i have to leave to go to the hospital i will be back later have fun

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.043046025187604931301073495306021606919706444365300504437700726938653476658540482895682023255731671008083253191134701531977327216262277734910301434073329657780176301162545225328061928920600009311905398639804126820396042450460066202697109907775276623968872853518354346016759166458978964531046772922079680334268349395400553907217843631670817062494745980159863699220055641618598527015369240922663513465449205721247877490866588987319843422033263068274836269183109480555389276190778038346967829969281182891390688896155908109741132615117268473730816500283359164264798601830326973866516776844628492169888293607239521260874661077748006501467554897266946929770167198202236168539094714436855125596965348850278428419408219121959065193321094260460012675282320096826009233318736492824372516701872916530191875274006751331906949469628695531029803522907150511237974426186839709893928853134757666263702066048826067502979089490242203757191931995294333171004695915352384474640644871822174241620572300156183558707078250717736961028156366959859921677655296330168740251591833351738043564377433284560158900338387796347112169428063480631538972184250753425370550017347776082214497306198063123186364841851403471408935730920459851486382788780998473732852005808994277131462002778650116911176327529356272603080102462324046604967312994263057368736624383919299458455699953933902352832256995941578134414743773382025255763658469026381866173288278447517255899658106552083051273359946737694651653754212906940384507355916630452196467129515987238021880606693829465264036899907307073437748560421341264116300230386978307277778110708808733561649284732562121195906834971751633631368677060936633119693654851223848615055082338939110035147213318136450234671212414029203616097230229945589841558040806845598058569001772383673629931716052342324341754195802753961257749189489037546944046112698324226187886768203898532477568362512929472764193781917650659658067589854223239462278187257059803948080557352654440583879422632096576531138731341885525844991796066351797621828730134725090944592790746734838522090756233976604544592665981142091966145661214078994176588123329399477109684347998836680683905444196796967903868455537458498586039586192714740410794873963813087940474907257329609557753515220359377337931228007810105449664070738053828013106422871266860404152807998523787092304682888264491432008554538300105320931903925794071312499192163207973053010023657157473954259657147335725251796830290146559452482096881004043699938653430179325321654494642446065202143276556976131126842569675581676839245919623228558247939229608790965820538400773470442008795867418950422510595413786972491033509552770587574679332977203196498537188583431130439956129081170636512351452788148050467473426861861103423636253521296569875953548170759645070796206682201768579959521236079495302391872041609223373410350948157764821209719094151213454012939429195884071063418582607938136555832992865478019751326416465650511040663018822058464400624606019400679681798288602527431886049034667225741015869049545764966156382561886172391332447947496644586519007980781117082080832021553420905696111049082685844767480840155238277177489208624726067851558869384426174647894231769867840866104268905410839849955133611554998133231555205769515722036852728601400019910791908069304128485748623142491012155998505368257654300095344895483194357030280508241289209799818268192667474541677114456558535733451965986362511131759065483735917201820897713058943975031526862863020430238708330397037864688223445598303312445818485142622513047532003550144078124831069189543160890852663608664354949670516059153261874952616358879968885489548737646622245041726345296829806734518932623185858874882546597909273541916936731698992217560436798479067580757234793907609041523948571053586384066337965273797847228760266551673618545481050809715004563792359718325107000073822179462358731590133936457251061372964290031222109669342316112331026823503833605565706502583832321627244774932094320883639781575056681178593042644061088809543333197948184330206660117244042299054620498800979659047820907097057396078391671915038011463035486300770242567590029510130760822673560320175464663608120374850039936697908449562312313298509745332308767805630772303120987386658714052978743556161615121774189061709715577455710161127856156620873018528092261285229010322165874979537115540211581972921040583292511405755187844636520805885692646019073556593713213213966061460742034317424610461043611879519537027747897267860975084431182515818098260712653832833939941816573348964437662757953006243481263581284433181109714025483815515348964930744099459782257197557903674741764225044035484415670530754237680782608356816059915546837787342603034767450416784886939340579307297735893890161000774744097698174116456513007650344673840749164573609437889867638252075539415406715721915296914731453346589790878646350370973001832566070316839486662669948238129199687090116537463734411569263617697006515197071129488492505811526009419472254401552612450606182107762414856252135950753135618729683159942855997294281110315350168393614610318114744974613446518541468264872922131535963094889967606125896648382597476027556006107102066564749867715245556119208056973521319244885469993060840556037400970969657521430843028156368845211529581718876773095256883200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 Is not so terrible a number

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hahahaha :)))) what did u use to get that?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Here's an interesting question, How many 0's are on the end of 13000! (factorial)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Is there something special about 13000!?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Nope, just a big number with a lot of 0's on the end of it.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I guess next year at number theory they will teach us this. But if you wish u could explain how to do it.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0About half that many.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Well, factorials are the product of the sequence of numbers from 1 to the number in question.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So to find how many 0's will be on the end, you need to find how many factors of 10 are in your product.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0And we know that 10 is the product of 5 and 2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Since every other number in the sequence will have at least one factor of 2, but only every 5th number will have a factor of 5 we can see that the limiting factor will be the 5's. (There will be at least one factor of 2 for each factor of 5 that can combine to make a factor of 10).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok, so we want to know how many factors of 5 are in the product 13000!, and that will be the same as the number of factors of 10, and the number of 0's at the end of our product.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0To find how many factors, we can rely on the fact that every 5th number will have at least 1 factor of 5. And of those that have 1 factor of 5, every 5th one of them will have a second factor, and so on.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0There are a few ways of determining this, but the one I like best is successive division.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sounds nice but I dont know what is it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0floor(13000/5) = 2600 floor(2600/5) = 520 floor(520/5) = 104 floor(104/5) = 20 floor(20/5) = 4 So there are 2600 + 520 + 104 + 20 + 4 = 3248 factors of 5 in 13000

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I see, it isnt that hard after all

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Not hard, just takes some thinking.

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0if you can read this and if you are interested

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0oh hey polpak this wasn't the cool problem i was talking about but this problem is cool lol
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