Real math analysis. Please Help solve this Problem. Problem 7.3.5. Show that if (an)n=1diverges to infinity then (a,)1 diverges.We will denote divergence to infinity aslim anto.However, strictly speaking this is an abuseof notation since the symbol ∞ does notrepresent a real number. This notationcan be very problematic since it looks somuch like the notation we use to denoteconvergence: lim an = a.Nevertheless, the notation is appropriatebecause divergence to infinity is "nice"divergence in the sense that it sharesmany of the properties of convergence, asthe next problem shows.

The given sequence ann=1∞ is diverges to infinity. That is limn→∞an=±∞. Without loss of generality,…

Answered: Problem 7.3.5. Show that if (an)n=1 =D1…

Math

Advanced Math

Problem 7.3.5. Show that if (an)n=1 =D1 diverges to infinity then (a,)1 diverges. 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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Question

Real math analysis. Please Help solve this Problem.

Problem 7.3.5. Show that if (an)n=1
diverges to infinity then (a,)1 diverges.
We will denote divergence to infinity as
lim an
to.
However, strictly speaking this is an abuse
of notation since the symbol ∞ does not
represent a real number. This notation
can be very problematic since it looks so
much like the notation we use to denote
convergence: lim an = a.
Nevertheless, the notation is appropriate
because divergence to infinity is "nice"
divergence in the sense that it shares
many of the properties of convergence, as
the next problem shows.

Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.

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