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Problem 7.3.4. Show that (n)=1 diverges to infinity.

Problem 7.3.4. Show that (n)=1 diverges to infinity.

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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Real math analysis. Problem 7.3.4 please.

10:54 O simple problem. Here's another way which highlights this particular type of divergence. First we'll need a new definition: Definition 7.3.3. A sequence, (an) n=1' diverges to positive infinity if for every real number r, there is a real number N such that n > N → an > r. A sequence, (a,n)=1, diverges to negative infinity if for every real number r, there is a real number N such that n > N = an < r. A sequence is said to diverge to infinity if it diverges to either positive or negative infinity. In practice we want to think of r| as a very large number. This definition says that a sequence diverges to infinity if it becomes arbitrarily large as n increases, and similarly for divergence to negative infinity. Problem 7.3.4. Show that (n)1 diverges to infinity. II II
Transcribed Image Text:10:54 O simple problem. Here's another way which highlights this particular type of divergence. First we'll need a new definition: Definition 7.3.3. A sequence, (an) n=1' diverges to positive infinity if for every real number r, there is a real number N such that n > N → an > r. A sequence, (a,n)=1, diverges to negative infinity if for every real number r, there is a real number N such that n > N = an < r. A sequence is said to diverge to infinity if it diverges to either positive or negative infinity. In practice we want to think of r| as a very large number. This definition says that a sequence diverges to infinity if it becomes arbitrarily large as n increases, and similarly for divergence to negative infinity. Problem 7.3.4. Show that (n)1 diverges to infinity. II II
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