5.5.3

[STARTS AT 5:47]

Instructor: First thing we want to do is consider the sum of the absolute value of negative 1 to the n plus 1 n over 2n cubed plus 1. Now, because n is positive, this is just equal to the sum from 1 to infinity of n over 2n cubed plus 1. 

Now, this is less than or equal to-- term for term-- n over-- yeah-- n cubed, which is the sum equals 1 over n squared. That converges. 

In this sequence-- or this series of the absolute value of negative 1 to the n plus 1 n over 2n cubed-- oh, actually, let's first discuss this because 1 over n squared converges. OK, because that converges, the sum, the absolute value of negative 1 to the n plus 1 n over 2n cubed plus 1, converges, and the sum from 1 to infinity of negative 1 to the n plus 1 n over 2n cubed plus 1 converges absolutely.