# What areas of physics depend on the sum $1 + 2 + 3 + 4 + 5 + 6+ 7+\ldots= -1/12$? [duplicate]

This youtube video from Numberphile, http://youtu.be/w-I6XTVZXww

shows how the value is derived. In the video, one interviewee claims that "this result is used in many areas of physics". In the video, only string theory is mentioned.

Which areas of physics use or depend on the sum $$1 + 2 + 3 + 4 + 5 + 6+ 7+\ldots= -1/12?$$

The sum $1+2+3+4+\ldots$ is not equal to $\frac{-1}{12}$. The series is divergent, and tends towards infinity, as the cameraman speculated near the start of the video.
However, $\frac{-1}{12}$ can be associated with the series $1+2+3+4+\ldots$, for example with analytic continuation. To quote the Wikipedia page on the subject: