Root Test
The Root Test is a method used to determine the convergence or divergence of an infinite series. It involves taking the n-th root of the absolute value of the terms in the series and analyzing the limit as n approaches infinity. If the limit is less than 1, the series converges; if it is greater than 1, the series diverges. If the limit equals 1, the test is inconclusive.
This test is particularly useful for series with terms raised to the power of n, such as those involving exponential functions or factorials. It provides a straightforward way to assess the behavior of series without needing to sum them directly.