AP Calculus BC glossary
Root test
The root test takes the limit of the nth root of the absolute value of the terms. A limit less than one means the series converges absolutely, greater than one means it diverges, and exactly one means the test tells you nothing.
It is the natural choice when the whole term is raised to the nth power, because the root cancels the exponent cleanly. For anything with factorials, the ratio test is easier.
Inconclusive at one
When the limit equals one the root test says nothing, and so does the ratio test, so you must switch to a comparison or the integral test.
Appears in: Unit 10: Infinite Sequences and Series (BC)