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-1 Suppose that (an), has an >0 for all n. Show that lim sup a, = (liminfa,)¯. Suppose (an)=1 and (bn)=1 are sequences of positive real numbers and lim sup an/bn < o. Prove that there is a constant M such that an < Mbn for all n> 1.

-1 Suppose that (an), has an >0 for all n. Show that lim sup a, = (liminfa,)¯. Suppose (an)=1 and (bn)=1 are sequences of positive real numbers and lim sup an/bn < o. Prove that there is a constant M such that an < Mbn for all 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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Suppose that (an) has an >0 for all n. Show that lim sup a, = (liminfa,). %3D Suppose (an)-1 and (bn)–1 are sequences of positive real numbers and lim sup an /bn <∞. Prove that there is a constant M such that a,n < Mb, for all n>1.
Transcribed Image Text:Suppose that (an) has an >0 for all n. Show that lim sup a, = (liminfa,). %3D Suppose (an)-1 and (bn)–1 are sequences of positive real numbers and lim sup an /bn <∞. Prove that there is a constant M such that a,n < Mb, for all n>1.
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