Nth term 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 diverges: This problem provides a series. The student is expected to use the nth term test to determine if the series diverges, or if there is not enough information to tell.Nthtt1.png

Strategies
Knowledge of sequence limits and the nth term test are encouraged to ensure success on this exercise.
 * 1) For a series to converge, the sequence must converge to zero. So if this doesn't happen, the series certainly diverges.
 * 2) This fact is commonly not stated as a separate test, but rather a first condition to check when seeing if a series converges.
 * 3) This test does not indicate the value of a series, only determines whether it diverges or not.

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.
 * 2) The harmonic series, 1/n, is a useful series that comes up in analysis and nature. It does not fail the nth term test, but it still diverges.