5 Questions
Which test compares a given series to a geometric series using the ratios of consecutive terms?
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 test is inconclusive
What does the Ratio Test indicate if the limit of the ratio of consecutive terms is a value such that |r| < 1?
The series converges
For large values of k, if $a_{k+1} \ approx ra_k$ for large k, what does this imply about the given series?
The series converges
What does it mean if a given series is approximately geometric for large k according to the Ratio Test?
The series converges
Test your understanding of convergence conditions for alternating series and the ratio test in calculus. This quiz covers when alternating series converge, how to test convergence without a simple integral or known series, and comparing series to geometric series using the ratios of consecutive terms.
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