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14. (A problem of Steinhaus) Consider the sequence beginning with x=1 and x = a which satisfies the recur- sion: Xn = Xn-2 - Xn-1 · %3D Find all values of a for which the sequence has only positive terms. [Hint: solve #12 first, and look carefully at how the sequence in #12 approaches its limit.]

14. (A problem of Steinhaus) Consider the sequence beginning with x=1 and x = a which satisfies the recur- sion: Xn = Xn-2 - Xn-1 · %3D Find all values of a for which the sequence has only positive terms. [Hint: solve #12 first, and look carefully at how the sequence in #12 approaches its limit.]

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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14. (A problem of Steinhaus) Consider the sequence beginning with x 1 and x= a which satisfies the recur- sion: %3D Find all values of a for which the sequence has only positive terms. [Hint: solve #12 first, and look carefully at how the sequence in #12 approaches its limit.]
Transcribed Image Text:14. (A problem of Steinhaus) Consider the sequence beginning with x 1 and x= a which satisfies the recur- sion: %3D Find all values of a for which the sequence has only positive terms. [Hint: solve #12 first, and look carefully at how the sequence in #12 approaches its limit.]
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