2. Σ(-1)" 8 n=1 an k=1 n n 3 n³ +2 3. Σ(-1)* k √n ³+2 k+ 3 k+7 2n+1 70 lim M-)D n n

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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Alternating Series Test part 2,3 Determine whether the following series converge or diverge. You must show that the series satisfies the necessary conditions in order to use the AST. If these condition arent satisfied, you’ll have to use a different test.
Alternating Series Test (AST)
If the numbers ak satisfy the three conditions:
• ak> 0 for all k (each ak is positive)
ak > ak+1 ({ak} is monotonically decreasing)
• lim ax = 0
k→∞
then the alternating series Σ (-1) ak converges.
k=0
Transcribed Image Text:Alternating Series Test (AST) If the numbers ak satisfy the three conditions: • ak> 0 for all k (each ak is positive) ak > ak+1 ({ak} is monotonically decreasing) • lim ax = 0 k→∞ then the alternating series Σ (-1) ak converges. k=0
3.
2.
an
8
8 W
Σ(-1)"
n=1
k=1
n=1
n
3
√n³ +2
n
√n ³+2
3
Σ(−1)kk + 3
k+7
14-1
✰
2n+1
70
2n11
Converges
2n+
n
lim
n->∞ √√√n ³+2
Transcribed Image Text:3. 2. an 8 8 W Σ(-1)" n=1 k=1 n=1 n 3 √n³ +2 n √n ³+2 3 Σ(−1)kk + 3 k+7 14-1 ✰ 2n+1 70 2n11 Converges 2n+ n lim n->∞ √√√n ³+2
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