Suppose r is a real number such that 0 < r|< 1. 1 (a) Show that there is a y > 0 such that |r| = 1+y 1 for all n E N. ny (b) Prove that |r"| < (c) Prove that {/nx"} converges to 0. (d) Prove that, if 0 < u < 1, then {nu"} converges to 0. [IIINT: For all n, nu" = (Vnu"/2)2.]
Suppose r is a real number such that 0 < r|< 1. 1 (a) Show that there is a y > 0 such that |r| = 1+y 1 for all n E N. ny (b) Prove that |r"| < (c) Prove that {/nx"} converges to 0. (d) Prove that, if 0 < u < 1, then {nu"} converges to 0. [IIINT: For all n, nu" = (Vnu"/2)2.]
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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Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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![Suppose r is a real number such that 0< r| < 1.
1
(a) Show that there is a y > 0 such that |r|
1+ y
(b) Prove that |2"| <
for all n E N.
ny
(c) Prove that {Vnx"} converges to 0.
(d) Prove that, if 0 < u < 1, then {nu"} converges to 0.
[IIINT: For all n, nu" = (Vnu"/2)2.]
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87a5eb21-df18-43d0-b53f-a372e6adca02%2F1d30f290-8f93-480a-b338-a86345c1abd2%2Fizon9k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose r is a real number such that 0< r| < 1.
1
(a) Show that there is a y > 0 such that |r|
1+ y
(b) Prove that |2"| <
for all n E N.
ny
(c) Prove that {Vnx"} converges to 0.
(d) Prove that, if 0 < u < 1, then {nu"} converges to 0.
[IIINT: For all n, nu" = (Vnu"/2)2.]
%3D
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