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In our sequence and series class, my teacher wrote this series and asked if it makes any sense. We all were saying "this makes no sense at all." But when I Googled it, the whole world knows it. So what exactly this series define? Some say string theory uses this series. Can someone explain it?

DMcMor
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Sulav Sigdel
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  • Many, many related questions: https://math.stackexchange.com/search?q=%5Cfrac%7B1%7D%7B12%7D – pjs36 Apr 16 '17 at 05:26
  • Giving a value to a divergent series. This is called regularisation. Many Cauchy-divergent series can be given a value if we change the conditions of convergence. – Zaid Alyafeai Apr 16 '17 at 05:31
  • If change the whole definition of summation of a series, see https://en.wikipedia.org/wiki/Divergent_series . In other words $\sum_{n\ge 1} n = + \infty$ but $\displaystyle{\overset{\mathcal{Z}}\sum_{n\ge 1}} n = -1/12$ where $\displaystyle\overset{\mathcal{Z}}\sum$ is a completly different symbol – reuns Apr 16 '17 at 05:33
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    Actually the post linked to, and all of the posts pjs36 linked to that weren't closed, don't give the firm negative answer that should be given to calculus students who happened upon this very misleading equation and are just looking for reassurance that mathematics actually makes sense. – Tim kinsella Apr 16 '17 at 05:38
  • Calculus curricula already make it hard enough to convince students and the general public that math has a perfectly logical foundation. – Tim kinsella Apr 16 '17 at 05:55
  • If the whole world knows it, the whole world is wrong. Basically, the logic is equivalent to "On weekdays a work in the 93rd floor as a brain surgeon. On weekends I garden on the ground floor. At 10:13 on weekdays I always run patients CAT scans. At 10:13 on weekends I always pull up weeds. Therefore whenever I run a CAT scan on the ground floor it consists of me pulling up weeds". Seriously, the logic is exactly that. – fleablood Apr 16 '17 at 07:26

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