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The Fibonacci Sequence is a recursively defined sequence determined by the function:
Fn = 0 if n = 0Fn = 1 if n = 1Fn-2 + Fn-1 if n ≥ 2
where n is a natural number.
The first few terms of the sequence are:F0 = 0, F1 = 1, F2 = 1, F3 = 2, F4 = 3, F5 = 5, F6 = 8, F7 = 13, F8 =21 .....
Consider the formula ( Fn)^2 + ( Fn+1 )^2 = F2n+1.
a) Show that the formula is true for n = 0 and n = 1.
b) Prove the formula is true for all natural numbers n by induction.
A gardener bought five geraniums, three rose bushes and four evergreen bushes from a nursery that had fourteen geraniums, twelve rose bushes and only five evergreen bushes. How many choices did the gardener have?
Three answers were given directly without any extra steps or explanation, essay. Factor the following expressions:
Simplify every statement form as a tautology, a contradiction, or neither.
Vertex and axis of symmetry from the graph.
Find the quotient and leave the result in a +bi form. 15(cos 240° + i sin 240°) / 3(cos 30° +i sin 30°). Find the angle between the given vectors, to the nearest tenth of a degree. u=5i + 6j, v = 3i -2j.
Consider the demand for computers. For each of the following, state the effect on demand: Consider the supply of computers. For each of the following, state the effect on supply:
Is the assumption "D is an integral domain" needed here? That is, does the conclusion hold if D is merely assumed to be a ring?
For each of the following pairs a and b, use the division algorithm to find quotient q and remainder r.
What is factoring by group? When do you factor a trinominal and why is it necessary to write the trinominal in four terms?
What was the percentage increase in motor vehicle production in countries outside the United States from 1950 to 1997?
Find the solution for x
Show that ~ is an euivalence relation on b. (The set of equivalence classes is called the direct or inductive limit of the directed system {A_i} and is denoted lim->A_i. For the rest of the problem let A=lim->A_i
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