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Example 4: Series with terms (ln n) / n diverges by the Integral Test - Hive - YouTube - Notes - Playlist - Sequences and Series

In this video, I show that the sum of the series with terms (ln n) / n diverges to infinity by computing its corresponding improper integral via the Integral Test. First noting that the natural logarithm function is continuous, and positive for x is greater than 1, then so is the corresponding function f(x) = (ln x) / x. However, it is uncertain whether the function is increasing or decreasing, so I take the derivative and show that it is negative for x is greater than the number e, thus the function itself is also decreasing. This allows us to apply the Integral Test for convergence and the corresponding improper integral approaches infinity, thus our series diverges!

#math #calculus #series #logarithms #education

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