Category:Nth Root Test

This category contains pages concerning Nth Root Test:

Let $\ds \sum_{n \mathop = 1}^\infty a_n$ be a series of real numbers $\R$ or complex numbers $\C$.

Let the sequence $\sequence {a_n}$ be such that the limit superior $\ds \limsup_{n \mathop \to \infty} \size {a_n}^{1/n} = l$.

Then:

If $l > 1$, the series $\ds \sum_{n \mathop = 1}^\infty a_n$ diverges.

If $l < 1$, the series $\ds \sum_{n \mathop = 1}^\infty a_n$ converges absolutely.