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..

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..

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TopNewestIt 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 – Achint Gupta · 3 years, 4 months ago

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hows this possible???? I mean sum of positive natural numbers is negative !!!!!! How ??? – Achint Gupta · 3 years, 4 months ago

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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- – Rushi Rokad · 3 years, 4 months ago

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– Anand Narayan · 3 years, 3 months ago

hey, that was grt proof.Log in to reply

– Rushi Rokad · 3 years, 3 months ago

Not mine..Log in to reply

– Achint Gupta · 3 years, 4 months 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 studiedLog in to reply

– Brij Rokad · 3 years, 4 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 .. ???Log in to reply

– Achint Gupta · 3 years, 4 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 functionLog in to reply

S1 = 1 + -1 +1 + -1 ...... S1 + S1 =( 1 + -1 + 1 + -1 + ...)+ ( 1 + -1 + 1 + -1...) 2 (S1) = 1 S1 = 1/2 ..Hence... – Rushi Rokad · 3 years, 4 months ago

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http://scientopia.org/blogs/goodmath/2014/01/17/bad-math-from-the-bad-astronomer/ – Achint Gupta · 3 years, 4 months ago

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– Rushi Rokad · 3 years, 4 months ago

Dat was Nice...Log in to reply

are u sure???....could u show the proof??? – Tanya Gupta · 3 years, 4 months ago

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– Rushi Rokad · 3 years, 4 months ago

Please see my reply to Achint Gupta..Log in to reply

– Tanya Gupta · 3 years, 3 months ago

Saw it...The numberphile video was amazing!!...Thanx!!Log in to reply