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.
<< Previous Example Section 8.3
Next Example >>
© Maplesoft, a division of Waterloo Maple Inc., 2023. All rights reserved. This product is protected by copyright and distributed under licenses restricting its use, copying, distribution, and decompilation.
For more information on Maplesoft products and services, visit www.maplesoft.com
Download Help Document