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 main objective when analyzing the given series?

• To calculate the first term of the series

• To identify the type of series

• To determine the interval of p for convergence

• To find the sum of the series

Which condition must be satisfied for an alternating series to converge?

• The first term must be greater than 10

• The series must have a common ratio greater than 1

• The limit of b sub n as n approaches infinity must be 0

• The series must be finite

In the context of the series, what role does p/10 play?

• It is the common ratio of a geometric series

• It is the first term of the series

• It is the upper limit of the series

• It is the sum of the series

What is the upper limit for p in the interval of convergence?

• p must be less than 10

• p must be equal to 10

• p must be less than 1

• p must be greater than 10

Why can't p be equal to 10 in the series?

• Because it would make the limit of b sub n non-zero

• Because it would make the series finite

• Because it would make the first term zero

• Because it would make the series diverge