Which of the following statements is true?

A. The Ratio Test says that the series converges absolutely.

B. The Ratio Test says that the series diverges.

C. The Ratio Test says that the series converges conditionally.

D. The Ratio Test is inconclusive, but the series converges absolutely by another test or tests.

E. The Ratio Test is inconclusive, but the series diverges by another test or tests.

F. The Ratio Test is inconclusive, but the series converges conditionally by another test or tests

Choose one or more options and explain why those options are true.

Question

Mathematics

Makai Conway

20 June, 10:19

Which of the following statements is true?

A. The Ratio Test says that the series converges absolutely.

B. The Ratio Test says that the series diverges.

C. The Ratio Test says that the series converges conditionally.

D. The Ratio Test is inconclusive, but the series converges absolutely by another test or tests.

E. The Ratio Test is inconclusive, but the series diverges by another test or tests.

F. The Ratio Test is inconclusive, but the series converges conditionally by another test or tests

Choose one or more options and explain why those options are true.

+4

Answers (1)

Know the Answer?

Rayne Neal · Answer 1

Answer: The correct option is C. The Ratio Test says that the series converges conditionally.

Step-by-step explanation:

Ratio test is used for testing convergence or divergence in series.

Iet consider a positive series

Summation a subscript n. £an

Let £an > 0.

Consider

Lim as n tends to infinity, 'a' subscript n+1 divided by 'a' subscript n = L

If L < 1 the series converges

If L >1 the series diverges

If L = 1 No conclusion.

The correct option is C because the series converges conditionally if L <1