Ratio Test

Equation
$$\lim_{n \rightarrow oo}\left | \frac{a_{n} + 1}{a_{n}}\right |$$

Use
 Calculate the limit as stated above. Once you have derived r follow these guidelines to determine convergence.  if $$r < 1$$ the series converges absolutely. if $$r > 1$$ the series is divergent. If $$r = 1$$the test was inconclusive. 

Explanation
By following the above equation to reach an outcome where $$r < 1$$ you are effectively showing that the terms of the target series will become less than a Geometric Series Test. Since anything less than a geometric series will converge you can tell that the target function will also. This is almost a diluted way ot using the direct comparison test with a geometric series.

Video Explanation


All Video Explanations by PatrickJMT