Convergence Tests for Series

What does it mean for a series to converge absolutely?

• The series converges only when all terms are positive.

• The series converges only when terms are negative.

• The series converges regardless of the sign of its terms.

• The series diverges when terms are negative.

What is the condition for a series to be conditionally convergent?

• The series converges, but its absolute value diverges.

• The series converges only when terms are negative.

• The series diverges regardless of the sign of its terms.

• The series converges only when terms are positive.

Which test is used to determine the convergence of the series in the example?

• Root Test

• Integral Test

• Comparison Test

• Ratio Test

What is the simplified form of the series used in the comparison test?

• 1/n^3

• 1/n^2

• 1/n

• 1/n^4

In the direct comparison test, what must be shown about a sub n and b sub n?

• a sub n is greater than b sub n

• a sub n is equal to b sub n

• a sub n is not related to b sub n

• a sub n is less than or equal to b sub n

Why is the series considered absolutely convergent in the direct comparison test?

• Because the series diverges.

• Because all terms are negative.

• Because the series is finite.

• Because the absolute value of the series converges.

What is the first step in applying the alternating series test?

• Check if the series is finite.

• Find the limit of a sub n as n approaches infinity.

• Ensure all terms are positive.

• Verify the series is geometric.

What must be verified about a sub n and a sub n+1 in the alternating series test?

• a sub n is not related to a sub n+1

• a sub n is less than or equal to a sub n+1

• a sub n is equal to a sub n+1

• a sub n is greater than a sub n+1

What conclusion is drawn from the alternating series test?

• The series is divergent.

• The series is conditionally convergent.

• The series is absolutely convergent.

• The series is finite.

What is the significance of the absolute value of a sub n in the alternating series test?

• It confirms the series is absolutely convergent.

• It indicates the series is geometric.

• It shows the series diverges.

• It determines if the series is finite.