Suppose {n}_1 and {wn}_1 are sequences of complex numbers such that limn→∞ ²n = 2 and limn→∞ Wn = w for some complex numbers z and w. Show that lim (Zn+wn) = z+w n→∞
Suppose {n}_1 and {wn}_1 are sequences of complex numbers such that limn→∞ ²n = 2 and limn→∞ Wn = w for some complex numbers z and w. Show that lim (Zn+wn) = z+w n→∞
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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![Suppose \(\{z_n\}_{n=1}^\infty\) and \(\{w_n\}_{n=1}^\infty\) are sequences of complex numbers such that \(\lim_{n \to \infty} z_n = z\) and \(\lim_{n \to \infty} w_n = w\) for some complex numbers \(z\) and \(w\). Show that
\[
\lim_{n \to \infty} (z_n + w_n) = z + w
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa62f7b35-7db6-46d8-92c3-a45ad2747ea7%2F1c65ac38-e489-4e98-8ece-8c355029f7fb%2Fyz0252_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose \(\{z_n\}_{n=1}^\infty\) and \(\{w_n\}_{n=1}^\infty\) are sequences of complex numbers such that \(\lim_{n \to \infty} z_n = z\) and \(\lim_{n \to \infty} w_n = w\) for some complex numbers \(z\) and \(w\). Show that
\[
\lim_{n \to \infty} (z_n + w_n) = z + w
\]
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