Examples on Identifying Geometric Series and Determining if it Converges or Diverges

In this video, I go over two examples and two methods of identifying if a series is a geometric series, and then finding its sum if it converges. In the first example, we are given the first 4 terms of a series, which we can identify the first term and calculate its common ratio from each successive term. Since the absolute value of the common ratio is less than 1, we can obtain its sum. I also illustrate in a graph how the partial sums of this series oscillate back and forth while ultimately approaching the limit of 3, which is defined as its actual sum.

In the second example, I re-arrange the summation equation directly to show that it is a geometric series. In this case, the common ratio is greater than 1, so the series diverges.

#math #calculus #series #geometricseries #education