It is currently 25 Nov 2017, 03:15

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# ASTOUNDING!!! What is 1 + 2 + 3 +4 + ...

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 42352

Kudos [?]: 133301 [3], given: 12445

ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

### Show Tags

31 Jan 2014, 01:41
3
KUDOS
Expert's post

Disclaimer: please do NOT apply this on the test!!! Very much out of scope!!!

What would you say is the value of 1 + 2 + 3 + 4 + 5 + ... to infinity ? I bet you'd be surprised to know it's:

[Reveal] Spoiler:
$$-\frac{1}{12}$$

_________________

Kudos [?]: 133301 [3], given: 12445

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4503

Kudos [?]: 8799 [0], given: 106

Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

### Show Tags

31 Jan 2014, 12:49
Bunuel wrote:

Disclaimer: please do NOT apply this on the test!!! Very much out of scope!!!

What would you say is the value of 1 + 2 + 3 + 4 + 5 + ... to infinity ? I bet you'd be surprised to know it's:

[Reveal] Spoiler:
$$-\frac{1}{12}$$

Bunuel,
This is great! It's funny the way those guys, physicists, talk about how the sum is "really" -1/12. Yes, that's really what it would be for Physicists, especially for String Theorists, but not at all what it would be for Mathematicians! This entire discussion really gets into some very profound areas --- the difference between the math used in Physics and the math used in pure Mathematics; the difference between operational mathematics and mathematical rigor; the deeply ambiguous nature of infinity and exactly what it means; the relationship of mathematical ideas to the physical world; etc. It think most students here would not appreciate that mathematics, far from being a totally cut-and-dry unambiguous field, is at higher levels very much a matter of multiple possibilities governed by convention and tastes. All this is well beyond the GMAT or anything particularly relevant to the business world, but it certainly is fascinating.
Thanks for posting this.
Mike
_________________

Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Kudos [?]: 8799 [0], given: 106

Manager
Joined: 11 Jan 2014
Posts: 94

Kudos [?]: 74 [0], given: 11

Concentration: Finance, Statistics
GMAT Date: 03-04-2014
GPA: 3.77
WE: Analyst (Retail Banking)
Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

### Show Tags

31 Jan 2014, 13:32
Mind blown!! :D

Thanks for sharing.

Kudos [?]: 74 [0], given: 11

Founder
Joined: 04 Dec 2002
Posts: 15886

Kudos [?]: 29134 [0], given: 5273

Location: United States (WA)
GMAT 1: 750 Q49 V42
Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

### Show Tags

31 Jan 2014, 15:22
So next time the bank calls me for the loan, I can just show them this video and give 8 cents? Or rather inform them that they owe me 8 cents to be exact... that will teach them!
_________________

Founder of GMAT Club

Just starting out with GMAT? Start here... or use our Daily Study Plan

Co-author of the GMAT Club tests

Kudos [?]: 29134 [0], given: 5273

BSchool Forum Moderator
Joined: 17 Sep 2013
Posts: 345

Kudos [?]: 149 [1], given: 96

Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

### Show Tags

01 Feb 2014, 13:06
1
KUDOS
Wooow.... Am I glad that I decided against becoming a physicist... Else wouldn't have got past the first chapter of the book...
_________________

Kudos [?]: 149 [1], given: 96

Current Student
Joined: 19 Sep 2012
Posts: 51

Kudos [?]: 34 [0], given: 0

GMAT 1: 750 Q51 V40
GPA: 3.8
Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

### Show Tags

01 Feb 2014, 14:13
This is amazing Bunuel! Love this kind of stuff. Do you have more of these videos?

Kudos [?]: 34 [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 42352

Kudos [?]: 133301 [0], given: 12445

Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

### Show Tags

02 Feb 2014, 02:27
JackDaniels wrote:
This is amazing Bunuel! Love this kind of stuff. Do you have more of these videos?

_________________

Kudos [?]: 133301 [0], given: 12445

Current Student
Joined: 19 Sep 2012
Posts: 51

Kudos [?]: 34 [0], given: 0

GMAT 1: 750 Q51 V40
GPA: 3.8
Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

### Show Tags

02 Feb 2014, 10:31
There is one little thing I do not fully understand in this equation. When he is calculating 2S(2), he shifts the second row a bit. On what ground is he allowed to do that?
I am probably missing something stupid ..

Kudos [?]: 34 [0], given: 0

Senior Manager
Status: Student
Joined: 26 Aug 2013
Posts: 252

Kudos [?]: 69 [0], given: 401

Location: France
Concentration: Finance, General Management
Schools: EMLYON FT'16
GMAT 1: 650 Q47 V32
GPA: 3.44
Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

### Show Tags

10 Feb 2014, 09:42
It gave me a headhache trying to understand... This is really complex...
_________________

Think outside the box

Kudos [?]: 69 [0], given: 401

Math Expert
Joined: 02 Sep 2009
Posts: 42352

Kudos [?]: 133301 [0], given: 12445

ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

### Show Tags

14 Jan 2015, 02:59
Bunuel wrote:

Disclaimer: please do NOT apply this on the test!!! Very much out of scope!!!

What would you say is the value of 1 + 2 + 3 + 4 + 5 + ... to infinity ? I bet you'd be surprised to know it's:

[Reveal] Spoiler:
$$-\frac{1}{12}$$

Why -1/12 is a gold nugget: https://www.youtube.com/watch?v=0Oazb7IWzbA by Professor Edward Frenkel
_________________

Kudos [?]: 133301 [0], given: 12445

Senior Manager
Status: Student
Joined: 26 Aug 2013
Posts: 252

Kudos [?]: 69 [0], given: 401

Location: France
Concentration: Finance, General Management
Schools: EMLYON FT'16
GMAT 1: 650 Q47 V32
GPA: 3.44
Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

### Show Tags

14 Jan 2015, 08:14
Just have an observation;

If you take the numbers they are taking, [1, 2, 3, 4], than 2S2 ==> 1 -2 + 1 + 3 - 2 - 4 + 3 - 4 This is exactly what they are saying in the video.

The result of this is not 1/4,as you can see but - 4. BUT they are using infinity. Therefore, here is where I got confuse. Since they are moving aside the second serie (to get the 1 - 1 + 1 ... ), it also shift the last number no? Therefore the last number must be moved aside too.

Example: if you go until 10, then your serie will be -10. And so forth until infinity. If the serie will go until 1, then the result will be 11.

In consequence, the last number is either + or - infinity.

S2 = + or - infinity.

Then, we know that S - S2 = 4S

So S = -S2/3

If S2 = + infinity then the result is negative and will not have any sense.

But if S2 = - infinity than S = + infinity, which make a bit more sense!

Thanks for this video again!
_________________

Think outside the box

Kudos [?]: 69 [0], given: 401

Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ...   [#permalink] 14 Jan 2015, 08:14
Display posts from previous: Sort by