In a number of tests for series convergence and divergence, you locate or calculate a quantity and draw conclusions based on its value. Here’s a table of which values give what conclusions, for five such tests. Note that the table assumes the series is of the correct form for the test to apply at all (although that is only a restriction on p-series and geometric series, in this instance).
| Test | Value to find | Convergent | Divergent | Inconclusive |
|---|---|---|---|---|
| test for divergence |  |
N/A | ≠ 0 | = 0 |
| p-series | p in  |
> 1 | ≤ 1 | N/A |
| geometric series | |r| in  |
< 1 | ≥ 1 | N/A |
| ratio test |  |
< 1 | > 1 | = 1 |
| root test | ![\lim_{n\to\infty} \sqrt[n]{|a_n|}](https://s0.wp.com/latex.php?latex=%5Clim_%7Bn%5Cto%5Cinfty%7D+%5Csqrt%5Bn%5D%7B%7Ca_n%7C%7D&bg=ffffff&fg=000&s=0&c=20201002 "\lim_{n\to\infty} \sqrt[n]{|a_n|}") |
< 1 | > 1 | = 1 |