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Mathematics, 13.03.2021 01:10 elijah4723
Recall that the Fibonacci Sequence is defined by the recurrence relation, a0 = a1 = 1 and for n ≥ 2, an = an−1 + an−2 . a. Show that f(x) = 1 1−x−x 2 is the generating function of the Fibonacci Sequence. b. Find and β such that 1 − x − x 2 = (1 − x)(1 − βx). c. Find A and B in terms of and β, such that 1 1−x−x 2 = A 1−x + B 1−βx. d. Use the results of the previous parts to obtain a formula for an.
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Recall that the Fibonacci Sequence is defined by the recurrence relation, a0 = a1 = 1 and for n ≥ 2,...
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