Chapter 8: Infinite Sequences and Series
Section 8.3: Convergence Tests
Determine if the series ∑n=1∞2⋅4⋅⋯⋅2 nn! diverges, converges absolutely, or converges conditionally.
If it converges conditionally, determine if it also converge absolutely.
Since the numerator of the general term in the series can be written as 2n⋅n!, this term is actually an=2n⋅n!/n=2n. Clearly, an→∞ as n→∞, so the series diverges by the nth-term test.
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