25.4. (a). Show that when 0 < || < 4, 1 1 8 zn 4z - z2 4z +Σ 4n+2* (b). Show that, when 0 < |z1|<2, n=() 2 1 8 (z - 1)(z - 3) - 3 2(z - 1) 3 Σ (2-1)" 27+2 n=0 (c). Show that, when 2<|z|< ∞, 1 z4+4z2 -*()*. n=0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 16E
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25.4. (a). Show that when 0 < || < 4,
1
1
8
zn
4z - z2
4z
+Σ
4n+2*
(b). Show that, when 0 < |z1|<2,
n=()
2
1
8
(z - 1)(z - 3)
- 3
2(z - 1)
3 Σ (2-1)"
27+2
n=0
(c). Show that, when 2<|z|< ∞,
1
z4+4z2
-*()*.
n=0
Transcribed Image Text:25.4. (a). Show that when 0 < || < 4, 1 1 8 zn 4z - z2 4z +Σ 4n+2* (b). Show that, when 0 < |z1|<2, n=() 2 1 8 (z - 1)(z - 3) - 3 2(z - 1) 3 Σ (2-1)" 27+2 n=0 (c). Show that, when 2<|z|< ∞, 1 z4+4z2 -*()*. n=0
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