Question

Does this series converge or diverege? State the method you used.

Answer 1

\[\sum_{1}^{\inf} \frac{ \ln(n) }{ 5n }\]

Answer 2

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Answer 3

Idea #1: Use the Ratio Test. Are you familiar with that?

Idea #2: Determine whether or not you could use the Comparison Test, with the test series being the harmonic series, (1/n). The harmonic series diverges, and [ln(n)] / n is larger than (1/n). What does that tell you about the convergence of ln(n)/5n?

Note that ln(n)/5n = (1/5)[ ln(n) / n].