Ratio test

The  exercise appears under the Integral calculus Math Mission. This exercise practices one of the series convergence/divergence tests.

Types of Problems
There is one type of problem in this exercise:


 * 1) ''Determine if the series converges or diverges: This problem provides a series. The student is expected to find the limit of the ratio of consecutive terms, then use the ratio test to determine if the series converges or diverges, or if there is not enough information to tell.Rattes1.png

Strategies
Knowledge of all limit tests, but specifically the ratio test, as well as experience with the limit of a sequence are encouraged to ensure success on this exercise.
 * 1) The ratio test finds the limit of the (n+1)th term over the nth term of a sequence.
 * 2) If the resulting limit is less than one, the original series converges.
 * 3) If the resulting limit is greater than one, the original series diverges.
 * 4) If the resulting limit is equal to one, then there is not enough information to determine whether the series converges or diverges and a different technique is required.
 * 5) This test only tells if a series converges, not what the value of the series will be.
 * 6) After obvious tests have been exhausted (like the nth term, geometric, and comparison tests), the ratio test is the can take care of most other cases.

Real-life Applications

 * 1) Real-life situations are not "exact" so approximating functions are used as models of real-life behavior in the sciences and economics. These concepts are used to create those approximating functions.