ME 0 X n=1 (-1)" n²e-n³/3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question

Determine whether the series converges absolutely, conditionally, or not at all.

8
Σ(-1)" n²e-n²³/3
2
n=1
Transcribed Image Text:8 Σ(-1)" n²e-n²³/3 2 n=1
Expert Solution
Step 1

Given series is ,

              n=1(-1)n n2 e-n3/3

(.)  A seriesn=1anis said to be absolutely         convergentif series n=1an is                   convergent.

(.)  Absolutely convergent series is                    always a convergent series .

(.)  If series  n=1an converges but series      n=1an diverges , then the series  n=1an    is called  conditionally convergent.

(.)  D' Alembert' s  Ratio test :                                                   If  n=1an is a series of positive terms such that limnanan+1=l  , then series  n=1an  is ,

(i)  convergent if  l>1                                      (ii)   divergent if  l<1                                      (iii)  test fails if  l =1                                      (iv)  convergent if  l = 

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