True-False Quiz Question 7: When the Ratio Test is Inconclusive

In this video I show that the Ratio Test can not be used to determine if the series with terms 1/n^3 converges or diverges. The ratio test states that if the limit as n approaches infinity of the absolute value of the ratio a_n+1 term / a_n is equal less than 1, it is convergent. If it is greater than 1 it is divergent. But if it is equal to 1 then it is inconclusive and no conclusion can be drawn about the convergence or divergence of the series. Applying the ratio test for our given series we get the limit approaching 1, which is inconclusive. Hence, the solution to our question is False and the ratio test can not be used to determine if our series converges or diverges.

Time stamps:

• Question 7: 0:00
• Solution: False: 0:15
• Applying the Ratio Test: 1:04
• Ratio Test = 1 = Inconclusive: 5:14

Full video below:

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