Suppose x is an accumulation point of (a,: n E J). Show that there is a subsequence of (a) that converges to x.
Suppose x is an accumulation point of (a,: n E J). Show that there is a subsequence of (a) that converges to x.
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 #35 please
Transcribed Image Text:35. Suppose x is an accumulation point of {a,: n E J). Show that there is a subsequence of
that converges to x.
(a)
*36. Let (an) be a bounded sequence of real numbers. Prove that (al has a convergent
subsequence. (Hint: You may want to use the Bolzano-Weierstrass Theorem.)
*37. Prove that if (a) decreasing and bounded, then (a,) converges.
38. Prove that if c> 1, then (Vc), converges to 1.
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