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?Determine whether the series is convergent or divergent. \(\sum_{n=2}^{\infty}
Chapter 9, Problem 24(choose chapter or problem)
QUESTION:
Determine whether the series is convergent or divergent.
\(\sum_{n=2}^{\infty} \frac{\ln n}{n^{2}}\)
Questions & Answers
QUESTION:
Determine whether the series is convergent or divergent.
\(\sum_{n=2}^{\infty} \frac{\ln n}{n^{2}}\)
ANSWER:Step 1 of 6
In the given problem it is asked to test whether the given series is convergent or divergent.
The series given is \(\sum_{n=2}^{\infty} \frac{\log n}{n^{2}}\). To test the convergence or divergence of the series, it is required to apply any of the tests for convergence. Here, integral test can be applied to test the convergence.
For this let \(f(x)=\frac{\log x}{x^{2}}\) be the function which is to be tested for decreasing property and positive nature.