The ratio test is a test in the

calculus of

sequences and

series for determining whether or not a series is

absolutely convergent:

For a series

inf
---
\ a_{n}
/__
n=1

if lim_{n->inf} |a_{n+1}/a_{n}| = L < 1, the series is absolutely convergent.

If lim_{n->inf} |a_{n+1}/a_{n}| = L > 1, the series diverges.

If lim_{n->inf} |a_{n+1}/a_{n}| = L = 1, the ratio test tells us nothing, and we must use another test.