1. Justify if the following series is conditionally convergent, absolutely convergent, or divergent +∞o (2) Σ n=2 1 √n(Inn)² +∞o η3/2 (b) Σ η3 n2 −n−1 n=1 +∞o cos(nn) (0) Σ 100 sin(n) + n n=2 80+

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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1.
too
1
(a)
√n(Inn)²
n=2
+∞o
72³/2
(b) Σ n3 n - n−1
n=1
+∞o
cos(NT)
(0) Σ
100 sin(n) + n
n=2
Justify if the following series is conditionally convergent, absolutely convergent, or
divergent
2. Find the largest real number R such that Σ" (1+1/n)-² converges for all |x| < R.
+oo
(d) Σ
(n=²)
n=1
+∞o
(e) Σcos(n) e-vi
n=1
1
1 1 1 1
(f) 1+
+...
2
4
5
6 7
+∞o
n=1
sec
133
=+=+=
8 | 1
Transcribed Image Text:1. too 1 (a) √n(Inn)² n=2 +∞o 72³/2 (b) Σ n3 n - n−1 n=1 +∞o cos(NT) (0) Σ 100 sin(n) + n n=2 Justify if the following series is conditionally convergent, absolutely convergent, or divergent 2. Find the largest real number R such that Σ" (1+1/n)-² converges for all |x| < R. +oo (d) Σ (n=²) n=1 +∞o (e) Σcos(n) e-vi n=1 1 1 1 1 1 (f) 1+ +... 2 4 5 6 7 +∞o n=1 sec 133 =+=+= 8 | 1
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