Problem 4. A student is trying to compare three infinite series, and they write: In(k) In(k) In(k) k3 - 1 k=1 k3 k=1 k3 + 1 k=1 1. They have made a mistake. Correctly order these three series from smallest to biggest. 2. Determine which (if any) of these three series converges. Be sure to describe the test or reasoning you used. Hint: You may use the fact that In(k) < k for all k > 1.
Problem 4. A student is trying to compare three infinite series, and they write: In(k) In(k) In(k) k3 - 1 k=1 k3 k=1 k3 + 1 k=1 1. They have made a mistake. Correctly order these three series from smallest to biggest. 2. Determine which (if any) of these three series converges. Be sure to describe the test or reasoning you used. Hint: You may use the fact that In(k) < k for all k > 1.
Chapter9: Sequences, Probability And Counting Theory
Section: Chapter Questions
Problem 25RE: Use the formula for the sum of the first nterms of a geometric series to find S9 , for the series...
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Transcribed Image Text:Problem 4. A student is trying to compare three infinite series, and they write:
In(k)
In(k)
In(k)
k3 - 1
k=1
k3
k=1
k3 +1
1. They have made a mistake. Correctly order these three series from smallest to biggest.
2. Determine which (if any) of these three series converges. Be sure to describe the test or
reasoning you used. Hint: You may use the fact that In(k) < k for all k > 1.
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