Prove the Root Property for Limits: Suppose {an} converges to a, an > 0 for each n E N, and m E N. Prove that {anm} converges to a/m. That is, prove that, if {am} is a sequence of non-negative terms, then for all m e N, lim Van = lim an n00 provided lim a, exists. (HINTS: • First, argue that, under the hypotheses, the number a must be non-negative. • Prove the result first in the case that a = = 0.
Prove the Root Property for Limits: Suppose {an} converges to a, an > 0 for each n E N, and m E N. Prove that {anm} converges to a/m. That is, prove that, if {am} is a sequence of non-negative terms, then for all m e N, lim Van = lim an n00 provided lim a, exists. (HINTS: • First, argue that, under the hypotheses, the number a must be non-negative. • Prove the result first in the case that a = = 0.
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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