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1. Let
for alla. Write down the values of a_{1}, a_{2} and a_{3}.
b. Write down the values of A(1), A(2) and A(3) defined by the recurrence relation: A(0) = -1, A(k) = 3A(k - 1) - 2k + 7, k \geq 1
c. Show that A(k) = a_{k} is a solution of the recurrence relation for all values of k \geq 1.
2. Write down all derangements of the set \left\{ a,b,c,d \right\} and show that the number of derangements is the same as predicted by the recurrence D(n) = (n - 1)(D(n - 2) + D(n - 1)) with initial values D(1) = 0 and D(2) = 1.
3. Solve the recurrence relation A(n) = 6A(n - 1) - 11A(n - 2) + 6A(n - 3) subject to initial values A(1) = 2, A(2) = 6, A(3) = 20.
[Latex fixing by bobbym]
Guys thanks for your help in advance.
I am planning to do a self study into discrete maths in preparation to computer science .... Algorithm analysis which I intend to do in 3 months ahead. I am not from a mathematics background so I need to prepare earlier.
could any good samaritan out there give me a list of the topics I should learn, in reference to this website(mathIsFun)?
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