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Alternating series Watch

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    So I've been experimenting in my free time with creating series that alternate. For example, ones where the series go 1, -1, 1, -1, ...

    However, I cannot for the life of me create one with alternate cubes (1, -8, 27, -64, 125, ...)

    Any help? Thanks.
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    (Original post by paradoxequation)
    So I've been experimenting in my free time with creating series that alternate. For example, ones where the series go 1, -1, 1, -1, ...

    However, I cannot for the life of me create one with alternate cubes (1, -8, 27, -64, 125, ...)

    Any help? Thanks.
    The sequence 1, -8, 27, -64 etc. is perfectly well defined (though divergent): the nth term is (-1)^(n+1) * n^3. Thus I don't see exactly what your issue is.
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    (Original post by paradoxequation)
    So I've been experimenting in my free time with creating series that alternate. For example, ones where the series go 1, -1, 1, -1, ...

    However, I cannot for the life of me create one with alternate cubes (1, -8, 27, -64, 125, ...)

    Any help? Thanks.
    As in writing it in the form \sum_{i=1}^{\infty} (-1)^{r+1}?
 
 
 
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