Thank you so much. But you put L<1 two timesWhen we use the ratio test, we find the limit:
The ratio test states that:
And so, because we require \(L<1\), the interval of convergence is necessarily open, that is, we do not include the end-points.
- if \(L<1\) then the series converges absolutely;
- if \(L<1\) then the series is divergent;
- if \(L=1\) or the limit fails to exist, then the test is inconclusive, because there exist both convergent and divergent series that satisfy this case.