True-False Quiz Question 8: Applying the Ratio Test to Show Convergence

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• Published on Jan 10, 2024

In this video I show that the series with terms 1/n! converges by the Ratio Test. The Ratio Test states that the limit as n approaches infinity of the absolute value of the ratio of terms a_n+1 / a_n converges if it equals to a number less than 1, diverges if greater than 1, and inconclusive if equal to 1. In our case, I show that the Ratio Test is equal to 0, which is less than 1. Hence our given series converges and the answer to the question is True.

Time stamps:

• Question 8: 0:00
• Solution: True: 0:15
• Ratio Test = 0 = Converges: 2:38

Full video below:

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