an+1 For the series ar suppose that lim = L. Prove the following: an n =1 If 0 1, the series diverges. If L = 1. The test is inconclusive. Give two examples of series for which, L = 1 and the first is convergent and the second is divergent.
an+1 For the series ar suppose that lim = L. Prove the following: an n =1 If 0 1, the series diverges. If L = 1. The test is inconclusive. Give two examples of series for which, L = 1 and the first is convergent and the second is divergent.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:QUESTION 3
an+1
For the series Eaw suppose that lim
an'
n =1
= [. Prove the following:
an
If 0<L<1, then the series converges absolutely.
If L> 1, the series diverges.
= 1, The test is inconclusive. Give two examples of series for which, L = 1 and the first is convergent and the second is divergent.
If L
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