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Re:The Ramanujan Summation: 1 and 2 and 3 and ⋯ + ∞ = -1/12 by fxj on Saturday August 03, 2019 @05:49AM (#20599535)
The value is the analytic continuation of Riemann's Zeta function at the argument -1.

https://en.wikipedia.org/wiki/Riemann_zeta_function

There are several methods to define finite sums for divergent series. See the wikipedia article for a comprehensive list:

https://en.wikipedia.org/wiki/Divergent_series

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