Solution Found!
Geometric series In Section 8.3, we established that the
Chapter 10, Problem 51E(choose chapter or problem)
QUESTION:
Geometric series In Section 8.3, we established that the geometric series \(\sum r^{k}\) converges provided |r| < 1. Notice that if -1 < r < 0, the geometric series is also an alternating series. Use the Alternating Series Test to show that for -1 < r < 0, the series \(\sum r^{k}\) converges.
Questions & Answers
QUESTION:
Geometric series In Section 8.3, we established that the geometric series \(\sum r^{k}\) converges provided |r| < 1. Notice that if -1 < r < 0, the geometric series is also an alternating series. Use the Alternating Series Test to show that for -1 < r < 0, the series \(\sum r^{k}\) converges.
ANSWER:Problem 51EGeometric series In Section 8.3,