-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
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F647c4828-40de-42b0-a5a4-728bbe00eecd%2Fa499fdbe-ca17-4d66-9ab2-14c6793a5eba%2Frpmdy0d_processed.jpeg&w=3840&q=75)
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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