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searching for Divergent geometric series 3 found (8 total)

alternate case: divergent geometric series

1 + 1 + 1 + 1 + ⋯ (677 words) [view diff] exact match in snippet view article find links to article

as a geometric series with the common ratio 1. For some other divergent geometric series, including Grandi's series with ratio −1, and the series 1 + 2

1 + 2 + 4 + 8 + ⋯ (1,194 words) [view diff] exact match in snippet view article find links to article

could have a negative value. A similar phenomenon occurs with the divergent geometric series 1 − 1 + 1 − 1 + ⋯ {\displaystyle 1-1+1-1+\cdots } (Grandi's series)

1 + 2 + 3 + 4 + ⋯ (4,231 words) [view diff] exact match in snippet view article find links to article

Euler's 1760 publication De seriebus divergentibus alongside the divergent geometric series 1 + 2 + 4 + 8 + ⋯. Euler hints that series of this type have finite