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Results tagged with divergent-series
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user 8955
Questions on whether certain series diverge, and how to deal with divergent series using summation methods such as Ramanujan summation and others.
10
votes
2
answers
464
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Checking my understanding: $1 - 1 + 1 - 1 + 1 - ... = \frac{1}{2}$
I've recently run into a proof that claims that $1 - 1 + 1 - 1 + 1 - 1 ... = \frac{1}{2}$ that proceeds as follows:
Let $S = 1 - 1 + 1 - 1 + 1 - 1 + ...$. Then $$S = 1 - (1 - 1 + 1 - 1 + 1 - 1 ... …
1
vote
0
answers
123
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Checking understanding of summations of divergent series [duplicate]
I recently learned about various techniques for summing divergent series. These techniques make it possible to show that, for example, $$1 + 2 + 3 + 4 + 5 + ... = \frac{-1}{12}.$$
I am a bit confused …