Grade 12 Mathematics Quiz on Infinite Series Tests

What is the nth term test for divergence used for?

• It is used to determine if an infinite series diverges by checking the sum of the first n terms as n approaches infinity.

• It is used to determine if an infinite series converges by checking the sum of the first n terms as n approaches infinity.

• It is used to determine if an infinite series diverges by checking the limit of the nth term as n approaches infinity.

• It is used to determine if an infinite series converges by checking the limit of the nth term as n approaches infinity.

What conclusion can be drawn for the series using the nth term test?

• The series oscillates

• The series converges

• The series could converge

• The series diverges

Explain the concept of the geometric series test.

• The geometric series test states that a geometric series with a common ratio |r| < 1 will diverge

• The geometric series test states that a geometric series with a common ratio |r| = 1 will converge

• The geometric series test states that a geometric series with a common ratio |r| < 1 will converge, while a series with |r| ≥ 1 will diverge.

• The geometric series test states that a geometric series with a common ratio |r| > 1 will converge

Describe when integral test for convergence of infinite series is applicable.

• The integral test is applicable when the series involves alternating terms.

• The integral test is applicable when the series involves negative terms and the terms are increasing.

• The integral test is applicable when the series involves terms that are not continuous.

• The integral test is applicable when the series involves positive terms and the terms are decreasing.

Determine the convergence or divergence of the series and justify your response.

• The series converges to 0

• The series diverges by the nth term test

• The series converges by the p-series test

• The series diverges by the geometric series test

When can the p-series test be used?

• The p-series test applies to series of the form Σ(1/p^n), where p is a variable

• The p-series test applies to series of the form Σ(1/p^n), where p is a constant

• The p-series test applies to series of the form Σ(1/n^p), where p is a constant.

• The p-series test applies to series of the form Σ(1/n^p), where p is a variable

Explain the relationship between the p-series test and the integral test for convergence of infinite series.

• The p-series test is a special case of the integral test

• The p-series test is used for alternating series while the integral test is used for non-alternating series

• The integral test is a special case of the p-series test

• The p-series test is completely unrelated to the integral test

• Converges by nth term test

• Diverges by nth term test

• Converges by geometric series test

• Diverges by geometric series test

• Converges by nth term test

• Diverges by nth term test

• Converges by geometric series test

• Diverges by geometric series test

• Converges by nth term test

• Diverges by nth term test

• Converges by geometric series test

• Diverges by geometric series test