Chapter 8: Infinite Sequences and Series
Section 8.3: Convergence Tests
Determine if the series ∑n=1∞nn2+2 diverges, converges absolutely, or converges conditionally.
If it converges conditionally, determine if it also converge absolutely.
For large n, n/n2+2 behaves like n/n=1, suggesting that the limiting behavior of an be tested by
limn→∞nn2+2 = 1
By the nth-term test, since an does not go to zero as n→∞, the series must necessarily diverge.
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