Convergence Tests for Series

Convergence Tests for Series

Assessment

Interactive Video

Mathematics

11th Grade - University

Practice Problem

Hard

Created by

Lucas Foster

FREE Resource

The video tutorial explains how to determine if an infinite series converges absolutely, conditionally, or diverges. It covers the comparison test and the alternating series test, providing examples and explanations for each. The tutorial emphasizes the importance of understanding the behavior of series terms and their absolute values to determine convergence.

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10 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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.

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

Root Test

Integral Test

Comparison Test

Ratio Test

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

1/n^3

1/n^2

1/n

1/n^4

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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.

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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.

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