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Is a divergent infinite series to the power of 2 also a divergent series?
Wiki User
∙ 13y ago
Not necessarily, and I'll give you an example.
The harmonic series, Σ∞n=1 (1/n), is divergent.
However, if you square (1/n) and use the result in the above series; i.e. Σ∞n=1 (1/n2), which is the p-series for p = 2, the result is that the series converges, and so therefore, by definition, is not divergent.
Wiki User
∙ 13y ago
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