In this lesson, we will learn how to determine whether a series is convergent or divergent by comparing it to a series of known convergence using the limit comparison test.
Students will be able to
Q1:
All the terms of the series ∞1𝑛tan are positive when 𝑛 is large since tan𝑥>0 when 𝑥>0 and close to 0. Use the limit comparison test to decide whether the series is convergent or divergent.
Q2:
Suppose 𝑎>0 and lim→∞√𝑛𝑎=𝑐 with 𝑐>0. What does the limit comparison test tell us about the series ∞𝑎?
Q3:
Let 𝑎=𝑛−7√𝑛+7𝑛−8 and consider the series ∞𝑎. We want to apply the limit comparison test.
Find 𝑝 so that lim→∞𝑎 is a positive constant.
Is the series convergent or divergent?
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