perplexus.info :: Just Math : Given the Function, Calculate the Value

Given the Function, Calculate the Value (Posted on 2023-08-08)

Each of A and B is a positive real number. Consider this function:

         A*B
A o B = -----
         A+B

Determine the value of:

2¹o(2²o(2³o ......o(2²⁰²² o 2²⁰²³)))

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

re: computer solution -- decimal version

| Comment 3 of 4 |

(In reply to computer solution by Charlie)

>> digits 3000

>> vpa(2)^2023 / (vpa(2)^2023 - 1)

ans =

1.000000000000000000000000000000000000000000000000000000000000000000000000000

00000000000000000000000000000000000000000000000000000000000000000000000000000

00000000000000000000000000000000000000000000000000000000000000000000000103829

02403136750072927708023522940034698371580487952967457167183754788462407907740

81318229532216534741588126084501161651158845707415144005427693226876620872152

03173664931026917072643320440166280842525526785520877726448024477613251368769

02868049980078025213210004376737661470351311846483759676542113015794145001585

68926949108143502565116521094665880759507226126207025954207021761929827460074

99481408188806861086746121777114713110569318188126290635608147944629268550139

86493291934333785514406026088156256146160156063070538454923987224489864257553

33855971409852825905221770999927603707076202536319911085649415152945135236996

47798309262098046466238657501197190816666519351557644944840080925569439493180

49755011494116839373312862884589016912650782034022874693669686974447413716287

96985128694958516976005954356037044689961349559120314846820191139837511226624

34063801475237077983233673423426146530671567107625057077207732535970015807537

30093503775469301663793166673279105103030728039143602222137100235025949346601

35810343095175825632940973942107055309071647058244425338584629647873791337255

16955551786788525136535926621240957868272745153576718024727485729391959701614

99824728688097344251939323140180583708864082393124994822443021068940387969469

88350636052789193078061476309045695525127432966201368359277464720944711282568

49668957527215180625142918179048708745818597205084604908529882974394559851802

43478196920329796194145819609542531260722895276826415825846793391182580384538

97573952673417099133581060134472290587078656186896274953759675963231688342046

49472518807594548419730206145830753542503337692534223177816831415809438270952

34309168554871482117181745497551342663750796365009877705608140433322405940640

52131628754241773535210939041065942941850252465199350538403299916759173516576

83719485848626362339625417770022099287511159437565997423122860900646971459792

05818764903425494036271879044922449732928916411978008804140156160542129712603

65275198641673031054503322703748024890266674466800654563149976873608590982780

91443203386463157121991875196203429848633401844496932613519889710811525012566

86192825670619336575130328915069068526749327920150637337250405131177077976793

49864590308104532581114602101197039932920955083418824195193884781115892888677

39515131345532797256952053951495826261224200571487599055503908771840747977782

754892930707643367690507356921448414589935176440011213039802646685792334499

Posted by Charlie on 2023-08-08 08:55:04

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