Series | Ratio Test: Another Full Example

The video tutorial explains how to determine the convergence of a series using the ratio test. It begins by introducing the series and the criteria for convergence. The instructor defines a sub n and calculates a sub n plus 1, then applies the ratio test to find the limit. The expression is simplified, and the limit is evaluated to conclude that the series converges absolutely.

What is the criterion for a series to absolutely converge using the limit L?

• L must be less than 1

• L must be greater than 1

• L must be less than or equal to 1

• L must be equal to 1

How do you find a_(n+1) from a_n in the given series?

• Replace n with n+1 in both numerator and denominator

• Add 1 to the denominator only

• Add 1 to the numerator only

• Multiply the entire expression by n+1

What is the first step in simplifying the expression for the ratio test?

• Cancel out all common terms immediately

• Break up the terms in the numerator and denominator

• Combine all terms into a single fraction

• Multiply the numerator by the denominator

Which terms cancel out when simplifying the expression for the ratio test?

• 4 to the 2n and n+1

• Negative 10 to the n and n+2

• Negative 10 to the n and 4 squared

• Negative 10 to the n and 4 to the 2n

What is the final value of the limit L after simplification?

• 10/16

• 1

• 0

• 16/10

What conclusion can be drawn if the limit L is less than 1?

• The series diverges

• The series converges absolutely

• The series is inconclusive

• The series converges conditionally

Which rule can be used to evaluate the limit of n+1 over n+2?

• Comparison Test

• Integral Test

• Ratio Test

• L'Hopital's Rule