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Here initial condition a(0) = 1,
(1 point) [3 Marks] Note that 0 € N. Give a recursive function f:N + N...
(1 point) (3 Marks] Note that 0 € N. Give a recursive function f:N → N that represents the sequence ao, 21, 22, az... if an 10n + 1. (1 point) [3 Marks] Find mod(31004 + 1004!, 11). A. I am finished this question
Note that 0 EN Give a recursive function f:N → N that represents the sequence ao, 21, 22, 23... if an 10n +1.
(1 point) [3 Marks] Note that 0 € N. Give a recursive function f: N N that represents the sequence ao, 21, 22, 23... if an= 5n + 1. A. I am finished this question
Let f:N + N be defined by the recursive definition: Base case: f(0) = 7 Recursive step: 3nf(n-1) and g:N + N be defined by the recursive definition: Base case: g(0) = 1 Recursive setep: g(n) = 8 * g(n-1) +4n Find a closed-form definition for fog(n)
Suppose f:N → N satisfies the recurrence f(n+1) = f(n) 7. Note that this is not enough information to define the function, since we don't have an initial condition. For each of the initial conditions below, find the value of f(7). a. f(0) = 1. $(7) = b. f(0) = 5. f(7) = c. f(0) = 19. f(7) = d. f(0) = 249. f(7) =
Let Σ = {0, 1). (a) Give a recursive definition of Σ., the set of strings from the alphabet Σ. (b) Prove that for every n E N there are 2" strings of length n in '. (c) Give a recursive definition of I(s), the length of a string s E Σ For a bitstring s, let O(s) and I(s) be number of zeroes and ones, respectively, that occur in s. So for example if s = 01001, then 0(s)...
Give a recursive definition of the sequence {an}, n = 1, 2, 3,... if an = n2 커-1, an-an-1+2n, for all n>1 어=1, an = an-1+2n-1, for all n21 an = an-1+2n-1. for all n21 gel, an=an-1+2n-1, for all n>1 -1, an- an-1+2n-1, for all n2o
3. The sequence (Fn) of Fibonacci numbers is defined by the recursive relation Fn+2 Fn+1+ F for all n E N and with Fi = F2= 1. to find a recursive relation for the sequence of ratios (a) Use the recursive relation for (F) Fn+ Fn an Hint: Divide by Fn+1 N (b) Show by induction that an 1 for all n (c) Given that the limit l = lim,0 an exists (so you do not need to prove that...
4. Define a function f:N → Z by tof n/2 if n is even 1-(n + 1)/2 if n is odd. f(n) = Show that f is a bijection. 11 ] 7. Let X = R XR and let R be a relation on X defined as follows ((x,y),(w,z)) ER 4 IC ER\ {0} (w = cx and z = cy.) Is R reflexive? Symmetric? Transitive? An equivalence relation? Explain each of your answers. Describe the equivalence classes [(0,0)]R and...
In Python 3 (2.5 pts] Write the recursive function thirtyTwos(n) that takes an integer greater or equal to 0 and returns an integer that represents the number of times that a 2 directly follows a 3 in the digits of n. Hint: The % and // operations from sumDigits could be helpful here >>> thirtyTwos (132432601)