Use Taylor series expansion of an appropriate function to prove the following equalities: (a) (b) n=1 n=1 n (n + 1)! 1 n!(n + 2) - = 1 1 [Hint: For part (a), differentiate the Maclaurin series of e²-¹. Part (b) follows from (a).] x
Use Taylor series expansion of an appropriate function to prove the following equalities: (a) (b) n=1 n=1 n (n + 1)! 1 n!(n + 2) - = 1 1 [Hint: For part (a), differentiate the Maclaurin series of e²-¹. Part (b) follows from (a).] x
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 44E
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![Use Taylor series expansion of an appropriate function to prove the following equalities:
(a)
(b)
Σ
n=1
∞
n=1
n
(n + 1)!
1
n! (n + 2)
= 1
=
1
2
[Hint: For part (a), differentiate the Maclaurin series of e*-¹. Part (b) follows from (a).]
X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbea85843-c685-4611-8e57-d8b3fe40f7ea%2F3da36e0c-c37c-4cd0-87ab-aacb90e6f050%2Fo1bu8ze_processed.png&w=3840&q=75)
Transcribed Image Text:Use Taylor series expansion of an appropriate function to prove the following equalities:
(a)
(b)
Σ
n=1
∞
n=1
n
(n + 1)!
1
n! (n + 2)
= 1
=
1
2
[Hint: For part (a), differentiate the Maclaurin series of e*-¹. Part (b) follows from (a).]
X
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