k=1 diverge or converge? If the sequence converges, find the limit. *45. Show that if x is any real number, there is a sequence of rational numbers converging to x. *46. Show that if x is any real number, there is a sequence of irrational numbers converging to x. 47. Suppose that (a) converges to A and that B is an accumulation point of {a,: n E J}. Prove that A = B.
k=1 diverge or converge? If the sequence converges, find the limit. *45. Show that if x is any real number, there is a sequence of rational numbers converging to x. *46. Show that if x is any real number, there is a sequence of irrational numbers converging to x. 47. Suppose that (a) converges to A and that B is an accumulation point of {a,: n E J}. Prove that A = B.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
#45 please
![[2=₁\√k² + n/]k=1
diverge or converge? If the sequence converges, find the limit.
*45. Show that if x is any real number, there is a sequence of rational numbers converging to x.
*46. Show that if x is any real number, there is a sequence of irrational numbers converging to x.
47. Suppose that (a) converges to A and that B is an accumulation point of {a,: nEJ).
Prove that A = B.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febf30032-6a45-43dc-84f6-3d2dba8b9144%2F9e159c5d-f81b-4387-9994-f6be9298c33a%2F6zxctw2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[2=₁\√k² + n/]k=1
diverge or converge? If the sequence converges, find the limit.
*45. Show that if x is any real number, there is a sequence of rational numbers converging to x.
*46. Show that if x is any real number, there is a sequence of irrational numbers converging to x.
47. Suppose that (a) converges to A and that B is an accumulation point of {a,: nEJ).
Prove that A = B.
Expert Solution
Step 1
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
