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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
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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[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.
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.
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