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*39. Suppose (x) converges to xo and (y) follows: 22nx, and 22n-1 = y Prove that (2)-1 converges to xo. converges to xo. Define a sequence (zn)-1 as

*39. Suppose (x) converges to xo and (y) follows: 22nx, and 22n-1 = y Prove that (2)-1 converges to xo. converges to xo. Define a sequence (zn)-1 as

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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1unin=1 subsequence. (Hint: You may want to use the Bolzano-Weierstrass Theorem.) *37. Prove that if (a) decreasing and bounded, then (an)-1 converges. 38. Prove that if c> 1, then (Vc), converges to 1. *39. Suppose (x)=1 converges to xo and (y) follows: 22n = x, and Z2n-1 = yn Prove that (2)-1 converges to xo. 40. Show that the sequence defined by a, 6 and a = √6 + a., for n > 1 is convergent. converges to xo. Define a sequence (zn)=1 as
Transcribed Image Text:1unin=1 subsequence. (Hint: You may want to use the Bolzano-Weierstrass Theorem.) *37. Prove that if (a) decreasing and bounded, then (an)-1 converges. 38. Prove that if c> 1, then (Vc), converges to 1. *39. Suppose (x)=1 converges to xo and (y) follows: 22n = x, and Z2n-1 = yn Prove that (2)-1 converges to xo. 40. Show that the sequence defined by a, 6 and a = √6 + a., for n > 1 is convergent. converges to xo. Define a sequence (zn)=1 as
Expert Solution
Step 1: Given

xnn=1∞ converges to x0

ynn=1∞ converges to x0

z2n=xnz2n-1=yn

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