Series | Alternating Series Test (Example 3): Finding Interval of p over which Series Converges

The video tutorial explores the convergence of an alternating series defined from n equals 1 to infinity of negative 1 to the n power times p over 10 raised to the n power. The goal is to determine the interval of p for which the series converges. The tutorial explains the criteria for convergence, focusing on the limit of b sub n as n approaches infinity. It analyzes the series as a geometric series, establishing that p over 10 must be less than 1 for convergence. The interval is determined to be 1 ≤ p < 10, with an explanation of why p cannot be 10.

What is the series being analyzed for convergence?

What values of p are likely to cause the series to diverge?

What is the condition for the limit of b sub n to ensure convergence of the alternating series?

Why must p be less than 10 for the series to converge?

Explain why p cannot be equal to 10 in the context of the series.