Calculus 2, Lecture 25A, Infinite Series Examples and Various Convergence Test Examples

Calculus 2, Lecture 25A: Infinite Series Examples and Various Convergence Tests.

(0:00) Career night soon.
(1:38) In the examples we will decide on convergence or divergence of each series and, if possible, give the sum when the series converges.
(3:19) Example 1: a series whose terms of the sum of the terms of two different geometric series (and start n at n = 4).
(10:22) Example 2: use the Ratio Test on a series involving factorials.
(19:48) Example 3: use both the Ratio Test and the Integral Test on a series that is the product of n and an exponential decay function of n. Use Mathematica to find the sum.
(28:10) Example 4: use the Alternating Series test for an alternating series related to a p-series with p = 1/2. Convergence is very slow (see this using Mathematica).