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5. If limn→∞ an 1 (a) limn→∞ bn (b) limn→∞ A and limno bn = B 0, prove B' an = bn B.

5. If limn→∞ an 1 (a) limn→∞ bn (b) limn→∞ A and limno bn = B 0, prove B' an = bn B.

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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5. If \(\lim_{n \to \infty} a_n = A\) and \(\lim_{n \to \infty} b_n = B \neq 0\), prove (a) \(\lim_{n \to \infty} \frac{1}{b_n} = \frac{1}{B}\), (b) \(\lim_{n \to \infty} \frac{a_n}{b_n} = \frac{A}{B}\).
Transcribed Image Text:5. If \(\lim_{n \to \infty} a_n = A\) and \(\lim_{n \to \infty} b_n = B \neq 0\), prove (a) \(\lim_{n \to \infty} \frac{1}{b_n} = \frac{1}{B}\), (b) \(\lim_{n \to \infty} \frac{a_n}{b_n} = \frac{A}{B}\).
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