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Using the last question, show that if {n}_₁ and {wn}_₁ are complex numbers such ∞ that 1ns and ₁wn = t for some complex numbers s and t, then Σ(²n+wn) = 8 + t ∞ n=1 ∞ n=1

Using the last question, show that if {n}_₁ and {wn}_₁ are complex numbers such ∞ that 1ns and ₁wn = t for some complex numbers s and t, then Σ(²n+wn) = 8 + t ∞ n=1 ∞ n=1

Advanced Engineering Mathematics
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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Please solve part b only

a) Suppose {n}1 and {wn}1 are sequences of complex numbers such that limn→∞ ²n = % and limn→∞ Wn = w for some complex numbers z and w. Show that lim (zn+wn) = z+w n→∞ b) Using the last question, show that if {zn}_₁ and {wn}1 are complex numbers such that 1 ²n = s and Σ₁ Wn = t for some complex numbers s and t, then n=1 Σ(²n + Wn) = 8 + t n=1
Transcribed Image Text:a) Suppose {n}1 and {wn}1 are sequences of complex numbers such that limn→∞ ²n = % and limn→∞ Wn = w for some complex numbers z and w. Show that lim (zn+wn) = z+w n→∞ b) Using the last question, show that if {zn}_₁ and {wn}1 are complex numbers such that 1 ²n = s and Σ₁ Wn = t for some complex numbers s and t, then n=1 Σ(²n + Wn) = 8 + t n=1
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