Convergence and divergence of series

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

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


 * 1) Determine if the series converges: This problem provides one or many series that may or may not converge. The student is asked to determine which of the series converge or diverge and answer questions related to the given series.Cadoser1.png

Strategies
Knowledge of geometric series and partial fractions are encouraged to ensure success on this exercise.
 * 1) This problem is about series, not sequences.
 * 2) A series converges if it the sequence of partial sums converges, so it can be embedded on the convergence and divergence of sequences.
 * 3) For a series to converge, the sequence it is representing must converge to zero.
 * 4) To find the limit of a geometric series, use g_1/(1-r).
 * 5) To find the limit of a telescoping sum, use partial fractions to split the rational expression and then combine like terms. On these problems the answer is often the first part of the first sum.

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.