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Questions and Answers
Which test compares a given series to a geometric series using the ratios of consecutive terms?
Which test compares a given series to a geometric series using the ratios of consecutive terms?
- Divergence Test
- Alternating Series Test
- Ratio Test (correct)
- Integral Test
If the limit of the ratio of consecutive terms of a given series approaches 1, what does it indicate according to the Ratio Test?
If the limit of the ratio of consecutive terms of a given series approaches 1, what does it indicate according to the Ratio Test?
- The series diverges
- The series converges
- The test is inconclusive (correct)
- The Ratio Test is invalid
What does the Ratio Test indicate if the limit of the ratio of consecutive terms is a value such that |r| < 1?
What does the Ratio Test indicate if the limit of the ratio of consecutive terms is a value such that |r| < 1?
- The series diverges
- The Ratio Test is invalid
- The series converges (correct)
- The test is inconclusive
For large values of k, if $a_{k+1} \ approx ra_k$ for large k, what does this imply about the given series?
For large values of k, if $a_{k+1} \ approx ra_k$ for large k, what does this imply about the given series?
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What does it mean if a given series is approximately geometric for large k according to the Ratio Test?
What does it mean if a given series is approximately geometric for large k according to the Ratio Test?
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