1+2+3+4+5+.... = ?

[Ketan Patel]

Dear all,

I hope you all are well and doing fine. If you are teaching Physics/Mathematics then you will enjoy throwing this puzzle to your students.

What is 1+2+3+4+... when summed up to the infinity? Surprisingly, the answer is -1/12 !!

This was known to the mathematicians for long time. Our genius mathematician Ramanujan proved this about 100 years ago. See (http://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF) for more details and for some ways to prove it.

This was however known as one of the mathematical trick and never got serious attention. However, recently this formula has been used by physicists (in string theory) and it turns out to be CORRECT as realized by some laws of Physics.

This tells us that things may not be as simple as we are trained to look at it. Second, every question in science is an important one.

You may throw this question to your students. Ask them to prove it in their way and also tell them to find out its use. I am sure it will be fun.

Best wishes,

Ketan

[Kathan Shukla]

Interesting! thanks for sharing, Ketan. Also, feeling very proud :D Ramanujan rocks!!

Kathan 

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[kausha...@yahoo.co.in]

Its really surprising. Interesting. Sent from Yahoo Mail on Android

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From: Ketan Patel <ketan....@gmail.com>;
To: PHYSICS_SPUVVN <physi...@googlegroups.com>;
Subject: 1+2+3+4+5+.... = ?
Sent: Sun, Jun 29, 2014 3:28:26 PM

[Manish Sanghani]

This is really an amazing series....

Manish

Manish Sanghani

Project Associate

Planetary Sciences Division

Physical Research Laboratory

Ahmedabad.

Telephone(O):  (+91)79-26314338

                      (+91)79-26314327

               (M): (+91)9898161464

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[Ketan Patel]

Yes, Kathan. Ramanujan was truely genius. May be, the main reason was that he was not formally "trained" and it helped him to develop his own vision and understanding of maths. So if you get a good teacher it is good, but if you get a bad teacher then it is really great. :)

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_________________________________________________________________

Ketan Patel
INFN, Sezione di Padova,                       Phone : (+39) 049 827 7192 (Office)
306, Theoretical Physics Group,                        : (+39) 049 869 8128 (Res.)
Dipartimento di Fisica "Galileo Galilei",              : (+39) 342 760 9909 (Mobile)
Via Marzolo 8, I-35131,
Padova, Italy.

_________________________________________________________________

[Jignesh Rathod]

Interesting facts!  With great proud that an indian mathematician had proved it..