Convergence and divergence of sequences

The  exercise appears under the Integral calculus Math Mission. This exercise determines whether various sequences converge or diverge.

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


 * 1) Determine if the sequences converge: This problem provides one or many sequences that may or may not converge. The student is asked to determine which sequences converge or diverge and answer questions related to the given sequence(s).Cadoseq1.png

Strategies
Knowledge of conditions for convergence and divergence, and limits approaching infinity are encouraged to ensure success on this exercise.
 * 1) This problem is about sequences, not series.
 * 2) A sequence converges if it approaches a finite value as n goes to infinity.
 * 3) For sequences involving ratios of functions, if the numerator is less than or equal to the denominator in magnitude, then the sequence will converge.
 * 4) Viewed as a function, the process for finding horizontal asymptotes can be used to find the limit of sequences.

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) Pattern recognition, as in sequences, is a skill that indicates high intelligence as measured by tests like the IQ test.