1/(2) = 0.5
1/(2+1/(2^2)) ~ 0.444444
1/(2+1/(2^2+1/(2^3))) ~ 0.445946
1/(2+1/(2^2+1/(2^3+1/(2^4)))) ~ 0.4459346186085498742665549036043587594300083822296730930427
1/(2+1/(2^2+1/(2^3+1/(2^4+1/(2^5))))) ~ 0.44593464052287581699346405228758169934640522875816993460
1/(2+1/(2^2+1/(2^3+1/(2^4+1/(2^5+1/(2^6)))))) ~ 0.4459346405122013659193048485766536161094695273096076952694
1/(2+1/(2^2+1/(2^3+1/(2^4+...(2^12+1/(2^13))))...))) ~ 0.445934640512202668119554340682617684270408845203438507903270858323956464392730999751675178678098540424040964828429
1/(2+1/(2^2+1/(2^3+1/(2^4+...(2^22+1/(2^23))))...))) ~ 0.445934640512202668119554340682617684270408845203438507903263560500661900691623277899777161890399214620424596104820554923366294796151748063663236645900848607009060104743783601449832729375348948615112656015450079555712557851878267028046756658939324736290632615562413506586188429610978503608522986699924808285347031488275550282237850708415604333199891972978281832787297452264977874623125894739627890243063456126267954299810109437168815453298185134311490899090710361
1/(2+1/(2^2+1/(2^3+1/(2^4+...(2^23+1/(2^24))))...))) ~ 0.445934640512202668119554340682617684270408845203438507903263560500661900691623277899777161890399214620424596104820554923366294796151748063663236645900848607009060104743783598486400590956716349929593771810009563841451238089219467415052571470942511914621194769633598516530215312086485688501973602785226945703751926675284633378339971224474985876675528550225632986664579269257396897935437125320337585612719140174752548254161741366681588707784288403942648803686583826
(1) 無限地加，商會否是 infinity ?
(2) 若不是，則數值為何？
( 可參 http://hk.knowledge.yahoo.com/question/question?qid=7011080301120 )
數學知識交流---繁分數
2011-09-03 5:36 am
回答 (4)
2011-09-07 5:33 pm
✔ 最佳答案
圖片參考：http://i212.photobucket.com/albums/cc82/doraemonpaul/yahooknowledge/continuedfraction/crazycontinuedfraction9.jpg
參考資料：
properties from http://en.wikipedia.org/wiki/Fundamental_recurrence_formulas + concept similar to http://tw.knowledge.yahoo.com/question/question?qid=1011072501482 + method from http://faculty.pccu.edu.tw/%7Emeng/Math15.pdf + http://en.wikipedia.org/wiki/Difference_equation#Solving_non-homogeneous_recurrence_relations + result from http://www.wolframalpha.com/input/?i=product1%2F%282%5E%28k-1%29-2%5E%28-k-1%29%29%2Ck%3D1+to+s + formula from http://en.wikipedia.org/wiki/Q-Pochhammer_symbol#Identities + http://mathworld.wolfram.com/q-PochhammerSymbol.html#eqn11 + my wisdom of maths
2011-09-05 12:36 am
Actually, some kind of computational knowledge engine can help you calculate some complicated maths question and give you exact values/answer correct to a certain d.p.
2011-09-03 6:05 am
TOP SECRET !
2011-09-04 14:56:40 補充：
I have told you ------------------------------------------------ SECRET
2011-09-04 14:56:40 補充：
I have told you ------------------------------------------------ SECRET
2011-09-03 6:00 am
lop, which calculator do u use so that u can get this?:
0.44593464051220266811955434068261768427040884520343850790326356050066190069162327789977716189039921462042459610482055492336629479615174806366323664590084860700906010474378359848640059095671634992959377181000956384145123808921946741505257147094
2011-09-02 22:17:37 補充：
lop,why do u cancel your ans in '2 mathematics Q. (20pt!!)' ??
are you giving up? D:
2011-09-04 13:06:25 補充：
lop, im trying to calculate this Q.
but those number given by u are really not enough for me...
can u pls tell me which calculator do u use?
PLS...D:
2011-09-04 19:10:35 補充：
im poor at computer..
0.44593464051220266811955434068261768427040884520343850790326356050066190069162327789977716189039921462042459610482055492336629479615174806366323664590084860700906010474378359848640059095671634992959377181000956384145123808921946741505257147094
2011-09-02 22:17:37 補充：
lop,why do u cancel your ans in '2 mathematics Q. (20pt!!)' ??
are you giving up? D:
2011-09-04 13:06:25 補充：
lop, im trying to calculate this Q.
but those number given by u are really not enough for me...
can u pls tell me which calculator do u use?
PLS...D:
2011-09-04 19:10:35 補充：
im poor at computer..
收錄日期: 2021-04-13 18:13:21
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110902000051KK00884