For which of the following infinite series does the Ratio Test fail? IM8 IM8 k=0 k 5k そそ n=1 (n + 1)! π + In 3 πT² ㅠ ㅠ + 27/3 37/3 In 4 πT3 + In 5 ㅠ 47/3 In 6 775 + . + ㅠ n7/3 + + In(k + 2) Tk+1 +

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
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For which of the following infinite series does the Ratio Test fail?
k=0
k
5k
nn
n=1 (n + 1)!
π +
π
27/3
+
+
π
37/3
+
+
ㅠ
7/3
4'
In 3
In 4
In 5
In 6
πT² 773 πTA T75
+
+
+
+
ㅠ
n7/3
+
+
In(k + 2)
πk+1
+
Transcribed Image Text:For which of the following infinite series does the Ratio Test fail? k=0 k 5k nn n=1 (n + 1)! π + π 27/3 + + π 37/3 + + ㅠ 7/3 4' In 3 In 4 In 5 In 6 πT² 773 πTA T75 + + + + ㅠ n7/3 + + In(k + 2) πk+1 +
The power series
xn
What is the power
n!
series representation of e(-²) ?
ex is
n=0
n=0
IM8 M8
None of the given choices
∞ (−1)n+¹ (x²n)
Σ
n!
n=0
n=0
(x²n)
n!
n=0
representation of
(−1)n (x²n)
n!
- (x²n)
n!
Transcribed Image Text:The power series xn What is the power n! series representation of e(-²) ? ex is n=0 n=0 IM8 M8 None of the given choices ∞ (−1)n+¹ (x²n) Σ n! n=0 n=0 (x²n) n! n=0 representation of (−1)n (x²n) n! - (x²n) n!
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