what is the exact value of e?

Answer 1

The constant e is base of the natural logarithm. To the 20th decimal place:

e ≈ 2.71828 18284 59045 23536

There are three basic definitions of e that give its exact value:

1. e = lim (n->infinity) {1 + 1/n}^n
2. e = SIGMA(n=0 -> n=infinity) {1/n!}
3. The unique real number e > 0 such that the integral from 1 to e over 1/t with respect to t is 1.

These definitions can be proved to be equivalent.

The first 999 digits are:

2.718 28182 84590 45235
36028 74713 52662 49775
72470 93699 95957 49669
67627 72407 66303 53547
59457 13821 78525 16642
74274 66391 93200 30599
21817 41359 66290 43572
90033 42952 60595 63073
81323 28627 94349 07632
33829 88075 31952 51019
01157 38341 87930 70215
40891 49934 88416 75092
44761 46066 80822 64800
16847 74118 53742 34544
24371 07539 07774 49920
69551 70276 18386 06261
33138 45830 00752 04493
38265 60297 60673 71132
00709 32870 91274 43747
04723 06969 77209 31014
16928 36819 02551 51086
57463 77211 12523 89784
42505 69536 96770 78544
99699 67946 86445 49059
87931 63688 92300 98793
12773 61782 15424 99922
95763 51482 20826 98951
93668 03318 25288 69398
49646 51058 20939 23982
94887 93320 36250 94431
17301 23819 70684 16140
39701 98376 79320 68328
23764 64804 29531 18023
28782 50981 94558 15301
75671 73613 32069 81125
09961 81881 59304 16903
51598 88851 93458 07273
86673 85894 22879 22849
98920 86805 82574 92796
10484 19844 43634 63244
96848 75602 33624 82704
19786 23209 00216 09902
35304 36994 18491 46314
09343 17381 43640 54625
31520 96183 69088 87070
16768 39642 43781 40592
71456 35490 61303 10720
85103 83750 51011 57477
04171 89861 06873 96965
52126 71546 88957 03503

You can get the first 10 million decimal places from http://67.49.215.31/constants.htm

Answer 2

E is irrational (actually, transcendental: there´s no polynomial with integer coefficients that admits e as a root). Therefore, the decimal expansion of e is infinite andf non periodic. We can't find the exact value of e.

Answer 3

Since e is transcendental, its exact value cannot be expressed in any finite number of digits. It is particularly easy to write a computer program to calculate as many digits as you please, however, and when I was in college (decades ago!) I ran off 12,000 digits just for fun. A computer with 256 MB of memory could bang out a hundred million digits without breathing hard.

Answer 4

maybe if you use the power series expansion,

e^x = sum {x^k/k!} , where k takes values from 0 to infinity.

so, e^1 = e = sum {1^k / k!} = 1 + 1/1! + 1/2! + ....

Answer 5

See this link for a method to calculate e to as many decimals places as you need:

Answer 6

e^ln(x) = x so the answer is 4/3

Answer 7

e is mc squared

Answer 8

wat is e here
try 2 be a little bit clear

Answer 9

Napier's Constant:

e = 2.718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427427466391932003059921817413596629043572900334295260595630738132328627943490763233829880753195251019011573834187930702154089149934884167509244761460668082264800168477411853742345442437107539077744992069551702761838606261331384583000752044933826560297606737113200709328709127443747047230696977209310141692836819025515108657463772111252389784425056953696770785449969967946864454905987931636889230098793127736178215424999229576351482208269895193668033182528869398496465105820939239829488793320362509443117301238197068416140397019837679320683282376464804295311802328782509819455815301756717361332069811250996181881593041690351598888519345807273866738589422879228499892086805825749279610484198444363463244968487560233624827041978623209002160990235304369941849146314093431738143640546253152096183690888707016768396424378140592714563549061303107208510383750510115747704171898610687396965521267154688957035035402123407849819334321068170121005627880235193033224745015853904730419957777093503660416997329725088687696640355570716226844716256079882651787134195124665201030592123667719432527867539855894489697096409754591856956380236370162112047742722836489613422516445078182442352948636372141740238893441247963574370263755294448337998016125492278509257782562092622648326277933386566481627725164019105900491644998289315056604725802778631864155195653244258698294695930801915298721172556347546396447910145904090586298496791287406870504895858671747985466775757320568128845920541334053922000113786300945560688166740016984205580403363795376452030402432256613527836951177883863874439662532249850654995886234281899707733276171783928034946501434558897071942586398772754710962953741521115136835062752602326484728703920764310059584116612054529703023647254929666938115137322753645098889031360205724817658511806303644281231496550704751025446501172721155519486685080036853228183152196003735625279449515828418829478761085263981395599006737648292244375287184624578036192981971399147564488262603903381441823262515097482798777996437308997038886778227138360577297882412561190717663946507063304527954661855096666185664709711344474016070462621568071748187784437143698821855967095910259686200235371858874856965220005031173439207321139080329363447972735595527734907178379342163701205005451326383544000186323991490705479778056697853358048966906295119432473099587655236812859041383241160722602998330535370876138939639177957454016137223618789365260538155841587186925538606164779834025435128439612946035291332594279490433729908573158029095863138268329147711639633709240031689458636060645845925126994655724839186564209752685082307544254599376917041977780085362730941710163434907696423722294352366125572508814779223151974778060569672538017180776360346245927877846585065605078084421152969752189087401966090665180351650179250461950136658543663271254963990854914420001457476081930221206602433009641270489439039717719518069908699860663658323227870937650226014929101151717763594460202324930028040186772391028809786660565118326004368850881715723866984224220102495055188169480322100251542649463981287367765892768816359831247788652014117411091360116499507662907794364600585194199856016264790761532103872755712699251827568798930276176114616254935649590379804583818232336861201624373656984670378585330527583333793990752166069238053369887956513728559388349989470741618155012539706464817194670834819721448889879067650379590366967249499254527903372963616265897603949857674139735944102374432970935547798262961459144293645142861715858733974679189757121195618738578364475844842355558105002561149239151889309946342841393608038309166281881150371528496705974162562823609216807515017772538740256425347087908913729172282861151591568372524163077225440633787593105982676094420326192428531701878177296023541306067213604600038966109364709514141718577701418060644363681546444005331608778314317444081194942297559931401188868331483280270655383300469329011574414756313999722170380461709289457909627166226074071874997535921275608441473782330327033016823719364800217328573493594756433412994302485023573221459784328264142168487872167336701061509424345698440187331281010794512722373788612605816566805371439612788873252737389039289050686532413806279602593038772769778379286840932536588073398845721874602100531148335132385004782716937621800490479559795929059165547050577751430817511269898518840871856402603530558373783242292418562564425502267215598027401261797192804713960068916382866527700975276706977703643926022437284184088325184877047263844037953016690546593746161932384036389313136432713768884102681121989127522305625675625470172508634976536728860596675274086862740791285657699631378975303466061666980421826772456053066077389962421834085988207186468262321508028828635974683965435885668550377313129658797581050121491620765676995065971534476347032085321560367482860837865680307306265763346977429563464371670939719306087696349532884683361303882943104080029687386911706666614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