Convergence Tests for Series

In this video, the instructor continues the discussion on determining the convergence or divergence of infinite series. The video reviews the limit comparison test from part one and introduces the ratio test as an alternative method. The instructor explains the steps to apply the ratio test, simplifies expressions, and calculates limits to confirm the series' convergence. The video concludes with a summary of the results, demonstrating that the series converges using both the limit comparison and ratio tests.

What was the main focus of part one of the series?

• Using the limit comparison test to determine convergence

• Using the ratio test to determine convergence

• Exploring the divergence of series

• Discussing the geometric series test

Which test does not require comparison to another series?

• Limit comparison test

• Geometric series test

• Integral test

• Ratio test

What is the first step in applying the ratio test?

• Calculating the limit of the absolute value of a(n+1)/a(n)

• Comparing with a known convergent series

• Finding the sum of the series

• Checking if the series is geometric

What happens if the limit L in the ratio test is less than one?

• The series diverges

• The series converges

• The test fails

• The series is geometric

In the given series, what is a(n) expressed as?

• 3n + 1 / n^2

• 3n + 1 / n

• 3n + 1 / n * 2^n

• 3n + 1 / 2^n

What simplification occurs with 2^n and 2^(n+1) in the ratio test?

• They simplify to zero

• They cancel out completely

• They remain unchanged

• They simplify to one factor of two

What is the degree of the numerator and denominator in the final limit calculation?

• Degree two

• Degree zero

• Degree one

• Degree three

What is the result of the ratio test for the given series?

• The series is geometric

• The series diverges

• The series converges

• The test is inconclusive

What is the final value of the limit calculated in the ratio test?

• 3/6

• 12

• 0

• 1

Which other test was mentioned as an alternative to the ratio test?

• Limit comparison test

• Harmonic series test

• Geometric series test

• Integral test