I repost this one last time to correct my previous post since I cant edit the orginal text. I thank everyone for their comments in the previous posts. A diverging infinite series doesnt have a value in its strict sense. However, one can extend/change the meaning of a diverging infinite series and use methods such as the Ramanujan summation, or the Cesaro summation (which can be used for step 1 of their proof), or use the Riemann zeta function and its analytical continuation to assign a value to this series. Since the video does not mention any of this, their statements becomes misleading. The infinite series of natural numbers diverges. So we cant actually assign a value to this sum in its original meaning. However, if we extend/change the meaning (which the video omits to state) and use e.g. one of the methods above (which the video also doesnt show), one arrives at the value -1/12. Of course, this still doesnt mean that the infinite series of the natural numbers converges to any value. So please dont throw your college math out of the window - its still valid. :-) Thank you again for the comments.
Posted on: Sat, 18 Jan 2014 17:52:03 +0000
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