# Amazing..!! How can this even be possible ??

Prove that:

1+2+3+4+5+6+.... up to infinity = -1/12 (negative of one-twelfth)

The above identity is used in many derivations of physics. I have a mathematical proof of the following, but please provide a logical one..

6 years, 3 months ago

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It took me 1 day to personally find out the mistakes that the university professors have done. Those people forgot the basic conditions required for treating a series as converging infinite series. In short this was just one stupid act of getting fame

- 6 years, 3 months ago

hows this possible???? I mean sum of positive natural numbers is negative !!!!!! How ???

- 6 years, 3 months ago

Let S1 = 1 + -1 + -1 + 1 + -1 .....up to infinity = 1/2 (this can be proved by using the sum of infinite GP and even by simpler method. Let S2 = 1 -2 +3 -4 + 5 -6...up to infinity S2 + S2 = (1 -2 +3 -4....)+ (0 +1 -2 +3..) =S1 Therefore, 2 S2 = S1 = 1/2 Therefore, S2=1/4

Let S3 = 1 + 2 + 3 + 4 + 5.... Now, S3 - S2 = (1 + 2 + 3 +4...) -(1 -2 +3 -4..) = 4 + 8 + 12 +16..... = 4 (1+ 2 +3 +4...) = 4 (S3) Therefore, 3 (S3) = - S2 S3 = -1/12...

Sorry,I could not present it properly here.... For a better explanation , watch Numberphile on Youtube - https://www.youtube.com/watch?v=w-I6XTVZXww&list=TLB3KTqn9SZmDUThXfkDzwmDz8PRN0U-K-

- 6 years, 3 months ago

hey, that was grt proof.

- 6 years, 2 months ago

Not mine..

- 6 years, 1 month ago

This stuff can never ever be proved by "using sum of infinite GP or by any other simple maths ". But I thank u for that video link which shows us but i cant understand it as it involves some higher mathematics which i haven't yet studied

- 6 years, 3 months ago

why can't we use sum of infinite GP..and take common ratio as -1 . we get the sum of the series as 1/2 .. ???

- 6 years, 3 months ago

To use sum of infinite GP we have a condition that | r | < 1 , where r denotes the common ratio and " | | " is the modulus function

- 6 years, 3 months ago

You can do it as such...

S1 = 1 + -1 +1 + -1 ...... S1 + S1 =( 1 + -1 + 1 + -1 + ...)+ ( 1 + -1 + 1 + -1...) 2 (S1) = 1 S1 = 1/2 ..Hence...

- 6 years, 3 months ago

I got really something interesting for u After reading through the below link, u will find that such things aren't possible .

- 6 years, 3 months ago

Dat was Nice...

- 6 years, 3 months ago

are u sure???....could u show the proof???

- 6 years, 3 months ago

- 6 years, 3 months ago

Saw it...The numberphile video was amazing!!...Thanx!!

- 6 years, 1 month ago