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10. Let (ao, a₁,.., aN) be a finite simple continued fraction. Define po = ao, P1 = a1a0 + 1, and Define and Prove that Pn = anpn-1 + Pn-2 90 = 1, 91 = a1, for n = 2,..., N. 1.3 The Euclidean Algorithm and Continued Fractions 23 In = angn-1 +9n-2 for n = 2,..., N. Pn qn (ao, a₁,..., an) = for n = = 0, 1,..., N. The continued fraction (ao, a₁,..., an) is called the nth convergent of the continued fraction (ao, a1,..., an).

10. Let (ao, a₁,.., aN) be a finite simple continued fraction. Define po = ao, P1 = a1a0 + 1, and Define and Prove that Pn = anpn-1 + Pn-2 90 = 1, 91 = a1, for n = 2,..., N. 1.3 The Euclidean Algorithm and Continued Fractions 23 In = angn-1 +9n-2 for n = 2,..., N. Pn qn (ao, a₁,..., an) = for n = = 0, 1,..., N. The continued fraction (ao, a₁,..., an) is called the nth convergent of the continued fraction (ao, a1,..., an).

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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10. Let (ao, a₁,..., ay) be a finite simple continued fraction. Define po = ao, P1 = a1a0 + 1, and Define and Prove that Pn anPn-1+Pn-2 90 = 1, 91 = a1, for n = 2,..., N. 1.3 The Euclidean Algorithm and Continued Fractions 23 qn = angn-1 +9n-2 for n = 2, ..., N. Pn qn (ao, a₁,..., an) = for n = = 0, 1,..., N. The continued fraction (ao, a₁,..., an) is called the nth convergent of the continued fraction (ao, a1,..., an).
Transcribed Image Text:10. Let (ao, a₁,..., ay) be a finite simple continued fraction. Define po = ao, P1 = a1a0 + 1, and Define and Prove that Pn anPn-1+Pn-2 90 = 1, 91 = a1, for n = 2,..., N. 1.3 The Euclidean Algorithm and Continued Fractions 23 qn = angn-1 +9n-2 for n = 2, ..., N. Pn qn (ao, a₁,..., an) = for n = = 0, 1,..., N. The continued fraction (ao, a₁,..., an) is called the nth convergent of the continued fraction (ao, a1,..., an).
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