Category:Ratio Test

This category contains pages concerning Ratio Test:

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

Let the sequence $\sequence {a_n}$ satisfy:

$\ds \lim_{n \mathop \to \infty} \size {\frac {a_{n + 1} } {a_n} } = l$

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

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