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n/Jn-1 35. Suppose x is an accumulation point of (a,: n E J). Show that there is a subsequence of (a) that converges to x. *36. Let (an) be a bounded sequence of real numbers. Prove that (an) has a convergent subsequence. (Hint: You may want to use the Bolzano-Weierstrass Theorem.) *37. Prove that if (an) decreasing and bounded, then (a) converges.

n/Jn-1 35. Suppose x is an accumulation point of (a,: n E J). Show that there is a subsequence of (a) that converges to x. *36. Let (an) be a bounded sequence of real numbers. Prove that (an) has a convergent subsequence. (Hint: You may want to use the Bolzano-Weierstrass Theorem.) *37. Prove that if (an) decreasing and bounded, then (a) converges.

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