11.6 Infinite Sequences & Series
Absolute Convergence & Ratio and Root Tests
Question #5 (Medium): Inconclusiveness According to the Ratio Test
There are only three outcomes to the ratio test:
1) | | means ∑ is absolutely convergent (ie. convergent)
2) | | , or means ∑ is divergent
3) | | means no conclusion can be drawn from the Ratio Test about convergence or
divergence of ∑
If the outcome is exactly 1, no conclusion can be drawn as to the series’ convergence or divergence.
For the following series, is the ratio test inconclusive, meaning it fails to give a definite answer?