Question: .......... 00 Let on = 1, a1 = 1 and on = an_1 + an_2 for all n 2 2. Let f(:::) = 2 aunt.

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00 Let on = 1, a1 = 1 and on = an_1 + an_2 for all n 2 2. Let f(:::) = 2 aunt\". Assume for now that this n=D series is absolutely convergent on some open interval around 0. (a) Using the recurrence relation, deduce that f (m) can be expressed as a rational function. (b) Use the method of partial fractions to deduce that x) = (him + m"; where (351, (352, A, B E R. (c) Expand the terms $1\"; + 95252 using the geometric series. (d) Give a reasonable argument to conclude that a,\" = 01112? + 021,03 for some 1121, 1122, 01, 02 E IR

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