Chapter 8: Infinite Sequences and Series

Section 8.3: Convergence Tests

Example 8.3.20

$$ Determine if the series $\sum _{n\=2}^{\infty }{\left(-1\right)}^n \frac{n}{\ln \left(n\right)}$ diverges, converges absolutely, or converges conditionally. If it converges conditionally, determine if it also converge absolutely. $$ Solution $$ Since $\underset{n\to \infty }{lim}\left|a_n\right|$ = $\underset{n\to \infty }{lim}n\/\ln \left(n\right)\=\infty$, the given series, even though it is alternating, cannot be convergent. It diverges by the nth-term test. $$

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