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
---
\ an
/__
n=1
if limn->inf |an+1/an| = L < 1, the series is absolutely convergent.
If limn->inf |an+1/an| = L > 1, the series diverges.
If limn->inf |an+1/an| = L = 1, the ratio test tells us nothing, and we must use another test.