How do you know when to use the Ratio Test for convergence?

It is not always clear-cut, but if a series contains exponential functions or/and factorials, then Ratio Test is probably a good way to go.

I hope that this was helpful.

The Ratio Test is used to determine the convergence or divergence of a series. It is particularly useful when dealing with series involving factorials or exponential functions. The Ratio Test states that if the limit of the absolute value of the ratio of consecutive terms of a series approaches a finite value ( L ) as ( n ) approaches infinity, then:

1. If ( L < 1 ), the series converges absolutely.
2. If ( L > 1 ) or ( L = \infty ), the series diverges.
3. If ( L = 1 ), the test is inconclusive, and other tests may need to be employed.

Therefore, the Ratio Test should be used when you have a series with terms that involve factorials or exponential functions, and you need to determine its convergence or divergence.