#1

my last thread about math was a throw away. let's do something cool.

1 = 1

1 + 1/2 = 1.5

1 + 1/2 + 1/3 = 1.8333..

1 + 1/2 + 1/3 + 1/4 = 2.08333...

1 + 1/2 + 1/3 + 1/4 + 1/5 = 2.28333...

1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 = 2.45

1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 = 2.59285714285714...

it's obviously getting bigger, but it seems to be slowing down. will it ever be bigger than 3? sure, just take it all the way out to 1/11 and it will just barely pass 3. what about 4? sure, take it out to 1/31.

okay let's talk bigger. can we get it bigger than 10? yes, keep adding up to and including 1/12,367. if you go as far as 1/1,000,000 you only reach about 14.4 though.

so is there a limit to this process? is there some number you can't reach? if so, what's the smallest number you can't reach? if not, why not?

and is there a better way to calculate these than just adding them up? is there a trick?

these are the questions fellas.

1 = 1

1 + 1/2 = 1.5

1 + 1/2 + 1/3 = 1.8333..

1 + 1/2 + 1/3 + 1/4 = 2.08333...

1 + 1/2 + 1/3 + 1/4 + 1/5 = 2.28333...

1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 = 2.45

1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 = 2.59285714285714...

it's obviously getting bigger, but it seems to be slowing down. will it ever be bigger than 3? sure, just take it all the way out to 1/11 and it will just barely pass 3. what about 4? sure, take it out to 1/31.

okay let's talk bigger. can we get it bigger than 10? yes, keep adding up to and including 1/12,367. if you go as far as 1/1,000,000 you only reach about 14.4 though.

so is there a limit to this process? is there some number you can't reach? if so, what's the smallest number you can't reach? if not, why not?

and is there a better way to calculate these than just adding them up? is there a trick?

these are the questions fellas.

#2

these are the sorts of questions that keep me up at night

#3

the smallest number you can't reach is 0

#4

69

turn the 9 upside down

66

6+6=12

one and two

1+2=3

so:

12-3=9

6

6

9

turn that 9 upside down again

666

turn the 9 upside down

66

6+6=12

one and two

1+2=3

so:

12-3=9

6

6

9

turn that 9 upside down again

666

#5

#7

9

1

1

#8

so is there a limit to this process? is there some number you can't reach? if so, what's the smallest number you can't reach? if not, why not?

well if you can keep going to infinity (with the fractions' denominator values), no matter how small the fractions get obvs you could still theoretically reach any number

and is there a better way to calculate these than just adding them up? is there a trick?

the fractions you're adding up as you go are decreasing exponentially or some shit (math isn't my strong suit anymore) so there's probably a way to simplify/condense it

or you could just write a computer program that does it for you automatically

i need more vodka for this brb

*Last edited by Dregen at Dec 7, 2014,*

#9

#10

I already showed the formula in that link. It's a pretty basic summation.

It's (Sigma/Summation) 1/n, where n=1 and it continues infinitely. They also show how it could theoretically move to infinity, being a divergent series. That's some basic higher level math.

It's (Sigma/Summation) 1/n, where n=1 and it continues infinitely. They also show how it could theoretically move to infinity, being a divergent series. That's some basic higher level math.

#11

#12

1 + 1 = 2

2 + 4 = 6

6 + 6 = 12

12 - 8 = 4

4 - 1 = 3

3 + 0 =3

3 = 3(1)

4(3) - 9 = 3

Half-Life 3 Confirmed

2 + 4 = 6

6 + 6 = 12

12 - 8 = 4

4 - 1 = 3

3 + 0 =3

3 = 3(1)

4(3) - 9 = 3

Half-Life 3 Confirmed

#13

here is another interesting question. why did you post this?

#14

here is another interesting question. why did you post this?

That implies that the first question was interesting.

#15

That implies that the first question was interesting.

sorry, what should i post about next? i really wanna get you going the way swan rape, flutes, and men's rights do.

#16

I remember doing this in uni math, it was fun shit.

#17

Is this what we're doing with threads, nowadays?my last thread about math was athrow away.

#18

here is another interesting question. why did you post this?

Weren't you supposed to be some math nerd? You should have known about such a basic series. Or this was a cheap attempt to carry over ancient ideas as your own.

Don't care either way.

#19

Weren't you supposed to be some math nerd? You should have known about such a basic series. Or this was a cheap attempt to carry over ancient ideas as your own.

Don't care either way.

this thread was for the intrigue of people who like puzzles. i have made a few of these before, just not lately.

(ps unless you wanna get pedantic about harmonic means, nothing here is ancient)

#20

if I take two small number (1 and 1 for instance) and put them together, I get a larger number (11)

maths

maths

#21

this thread was for the intrigue of people who like puzzles. i have made a few of these before, just not lately.

(ps unless you wanna get pedantic about harmonic means, nothing here is ancient)

K.

I was only confirming.

#22

2 + 2 = 5

#23

the set of real numbers is infinite but not countably so

from that, my intuition is that yes you would reach a point where adding smaller and smaller numbers would not breach the next integer

from that, my intuition is that yes you would reach a point where adding smaller and smaller numbers would not breach the next integer

#24

johnny had 1 pizzas now he has none, how many pizzas does he have?

#25

You can get it to any number doing that.

You're gonna run out of room on the chalkboard trying though.

You're gonna run out of room on the chalkboard trying though.

*Last edited by stratkat at Dec 7, 2014,*

#26

the set of real numbers is infinite but not countably so

from that, my intuition is that yes you would reach a point where adding smaller and smaller numbers would not breach the next integer

interesting thought. you're totally right that the values achieved by the subseries must be countable (since the op gives the exact method of counting them) but that does not necessarily imply it's bounded. for example, the rationals are countable but unbounded.

since i know you're familiar with calculus, i think i can convince you it's unbounded with a single picture from wikipedia.

ya?

#27

right we're doing rational numbers not just real numbers in general

hmmmmmmmmmm

hmmmmmmmmmm

#28

#29

lets see

since its unbounded, we can say that at any point in the series there are an infinite number of non-negative successors

which is more than enough to add em all up together and reach the floor of the next whole number

so now how do you compute this efficiently

since its unbounded, we can say that at any point in the series there are an infinite number of non-negative successors

which is more than enough to add em all up together and reach the floor of the next whole number

so now how do you compute this efficiently

#30

if you come up with a good technique, publish it

~~

~~

#31

it's already O(n)

gonna be hard to beat

gonna be hard to beat

#32

it's already O(n)

gonna be hard to beat

so my favorite mathematical constant, at the center of my area of interest, is calculated with a formula involving the subseries in the OP. you can see the limit expression here. if i set n to 10,000,000 and slap it into mathematica, it takes around 10 minutes and only produces a handful of correct digits.

there is a refined limit formula that converges faster, but it's still painfully slow. this is only one example, but you can imagine that among the others that exist there is interest in understanding a computation method faster than O(n) so that maybe it can be extended to more pertinent problems.

#33

so i ran some thought experiments in python and quickly realized that more than a time complexity issue this is a space complexity issue

#34

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198938095257201065485863278865936153381827968230301952035301852968995773622599413891249721775283479131515574857242454150695950829533116861727855889075098381754637464939319255060400927701671139009848824012858361603563707660104710181942955596198946767837449448255379774726847104047534646208046684259069491293313677028989152104752162056966024058038150193511253382430035587640247496473263914199272604269922796782354781636009341721641219924586315030286182974555706749838505494588586926995690927210797509302955321165344987202755960236480665499119881834797753566369807426542527862551818417574672890977772793800081647060016145249192173217214772350141441973568548161361157352552133475741849468438523323907394143334547762416862518983569485562099219222184272550254256887671790494601653466804988627232791786085784383827967976681454100953883786360950680064225125205117392984896084128488626945604241965285022210661186306744278622039194945047123713786960956364371917287467764657573962413890865832645995813390478027590099465764078951269468398352595709825822620522489407726719478268482601476990902640136394437455305068203496252451749399651431429809190659250937221696461515709858387410597885959772975498930161753928468138268683868942774155991855925245953959431049972524680845987273644695848653836736222626099124608051243884390451244136549762780797715691435997700129616089441694868555848406353422072225828488648158456028506016842739452267467678895252138522549954666727823986456596116354886230577456498035593634568174324112515076069479451096596094025228879710893145669136867228748940560101503308617928680920874760917824938589009714909675985261365549781893129784821682998948722658804857564014270477555132379641451523746234364542858444795265867821051141354735739523113427166102135969536231442952484937187110145765403590279934403742007310578539062198387447808478489683321445713868751943506430218453191048481005370614680674919278191197939952061419663428754440643745123718192179998391015919561814675142691239748940907186494231961567945208095146550225231603881930142093762137855956638937787083039069792077346722182562599661501421503068038447734549202605414665925201497442850732518666002132434088190710486331734649651453905796268561005508106658796998163574736384052571459102897064140110971206280439039759515677157700420337869936007230558763176359421873125147120532928191826186125867321579198414848829164470609575270695722091756711672291098169091528017350671274858322287183520935396572512108357915136988209144421006751033467110314126711136990865851639831501970165151168517143765761835155650884909989859982387345528331635507647918535893226185489632132933089857064204675259070915481416549859461637180270981994309924488957571282890592323326097299712084433573265489382391193259746366730583604142813883032038249037589852437441702913276561809377344403070746921120191302033038019762110110044929321516084244485963766983895228684783123552658213144957685726243344189303968642624341077322697802807318915441101044682325271620105265227211166039666557309254711055785376346682065310989652691862056476931257058635662018558100729360659876486117910453348850346113657686753249441668039626579787718556084552965412665408530614344431858676975145661406800700237877659134401712749470420562230538994561314071127000407854733269939081454664645880797270826683063432858785698305235808933065757406795457163775254202114955761581400250126228594130216471550979259230990796547376125517656751357517829666454779174501129961489030463994713296210734043751895735961458901938971311179042978285647503203198691514028708085990480109412147221317947647772622414254854540332157185306142288137585043063321751829798662237172159160771669254748738986654949450114654062843366393790039769265672146385306736096571209180763832716641627488880078692560290228472104031721186082041900042296617119637792133757511495950156604963186294726547364252308177036751590673502350728354056704038674351362222477158915049530984448933309634087807693259939780541934144737744184263129860809988868741326047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#35

can we use the fact that

1/n = 1/(n-1) - 1/(n^2-n)

for n >= 2 obvi

group some of this stuff together maybe

1/n = 1/(n-1) - 1/(n^2-n)

for n >= 2 obvi

group some of this stuff together maybe

*Last edited by Godsmack_IV at Dec 7, 2014,*

#36

:0