Chapter 8: Infinite Sequences and Series
Section 8.3: Convergence Tests
Determine if the series ∑n=1∞−1n+1n n diverges, converges absolutely, or converges conditionally.
If it converges conditionally, determine if it also converge absolutely.
Since the series is alternating, it is a candidate for the Leibniz test. Now an=1/n3/2, which generates a sequence that is monotone decreasing to zero as n→∞. Hence, by this test, the series converges conditionally.
Moreover, since Σ an is a p-series with p=3/2>1, the series converges absolutely.
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