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(4) Suppose xo = 2√√3, yo = 3, Xn= 2xn-19n-1 Xn-1+Yn-1 and Prove that (a) xnx and yn ↑y as n→ ∞o for some x, y € R; (b) x=y and 3.14155 < x < 3.14161. (x is actually ) Yn = √√xn Yn- for all ne N. Note: If (xn) is monotonically decreasing (resp. montonically increasing) and converges to x then we write xnx (resp. xnx). Thus, proving this requires the use of the Monotone Convergence Theorem.

(4) Suppose xo = 2√√3, yo = 3, Xn= 2xn-19n-1 Xn-1+Yn-1 and Prove that (a) xnx and yn ↑y as n→ ∞o for some x, y € R; (b) x=y and 3.14155 < x < 3.14161. (x is actually ) Yn = √√xn Yn- for all ne N. Note: If (xn) is monotonically decreasing (resp. montonically increasing) and converges to x then we write xnx (resp. xnx). Thus, proving this requires the use of the Monotone Convergence Theorem.

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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(4) 2√3, yo = 3, Suppose xo 2v Xn = 2xn-1Yn-1 Xn-1+Yn-1 and Prove that (a) xnx and yn ↑y as n→ ∞o for some x, y € R; (b) x = y and 3.14155 < x < 3.14161. (x is actually л) Yn = √√xn Yn-1 for all n E N. Note: If (xn) is monotonically decreasing (resp. montonically increasing) and converges to x then we write xnx (resp. xnx). Thus, proving this requires the use of the Monotone Convergence Theorem.
Transcribed Image Text:(4) 2√3, yo = 3, Suppose xo 2v Xn = 2xn-1Yn-1 Xn-1+Yn-1 and Prove that (a) xnx and yn ↑y as n→ ∞o for some x, y € R; (b) x = y and 3.14155 < x < 3.14161. (x is actually л) Yn = √√xn Yn-1 for all n E N. Note: If (xn) is monotonically decreasing (resp. montonically increasing) and converges to x then we write xnx (resp. xnx). Thus, proving this requires the use of the Monotone Convergence Theorem.
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