Problem 3: Define the integer sequences (n)-1 and (yn) byXn+Yn √2 = (3+2√2)"(So x₁ = 3 and y₁ = 2. And since (3+2√2)² = 17 + 12√2, we getx₂ = 17 and y2 = 12. Etc.) Show thatx² - 2y² = 1for all n € N.

Answered: Image /qna-images/answer/f70ffdca-a1df-40b9-91e4-788244af8925.jpg

Answered: Problem 3: Define the integer sequences…

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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can you break down this sequence a bit more - i'm not understanding how the numerator went to 1 all of a sudden and the denominator as well
The first four terms of the sequence (Xn) are given by X1 = 1, X2 = 5, X3 = 21, X4= 85. Therefore, the sequence (Xn) is given as follows. OA X = (n- 1)² +1 O B. X1 =1 and X = 3n + 6 for n > 2 Oc X, =(4" - 1) O D. X, = 2n – 1 O E X = 1/(2n + 1) Next page Link to: Elementary Jump to... Analysis, 2nd Edition O Tyne here to search
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Problem 3: Define the integer sequences (n)-1 and (yn) by Xn+Yn √2 = (3+2√2)" (So x₁ = 3 and y₁ = 2. And since (3+2√2)² = 17 + 12√2, we get x₂ = 17 and y2 = 12. Etc.) Show that x² - 2y² = 1 for all n € N.