(4) Suppose xo = 2√3, yo = 3, Prove that 2xn-14-1 Xn-1+Yn-1 and Yn √n Yn-1 for all n € N. = (b) x = y and 3.14155

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Chapter2: Second-order Linear Odes
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(4)
Suppose xo = 2√3, yo = 3,
Prove that
Xn
2xn-14-1
Xn-1+Yn-1
and
Yn √n Yn-1 for all n € N.
(b) x = y and 3.14155 <x<3.14161. (x is actually )
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.
B
Transcribed Image Text:(4) Suppose xo = 2√3, yo = 3, Prove that Xn 2xn-14-1 Xn-1+Yn-1 and Yn √n Yn-1 for all n € N. (b) x = y and 3.14155 <x<3.14161. (x is actually ) 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. B
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