Calculus 2, Lec 25B, Alternating Series Test Error Estimate, Power Series, Interval of Convergence

Calculus 2, Lecture 25B.

(0:00) Example 1: Alternating series test error bound and its use to approximate the sum of an alternating series to within a specified tolerance.
(4:19) Example 2: series whose terms are ln(n)/n diverges by the Integral Test (the Comparison Test could also be used...compare it with the Harmonic Series).
(8:00) Example 3: series whose terms are 1/(n*ln(n)) also diverges by the Integral Test.
(10:31) Power series centered at x = a, often treating x as a variable to get a function of x.
(13:25) Example 4: sum of (x-3) to the nth power divided by n + 1. Use the Ratio Test to find values for which the series definitely converges and definitely diverges (and get the radius of convergence), then check the endpoints separately to get the interval of convergence.
(27:31) Example 5: sum of x to the nth power divided by n factorial. Find the interval and radius of convergence.