Find the solution for each of the following recurrences, and then give tight bounds (i.e., in Θ(·)) for T (n). (a) T (n) = T (n − 1) + 1/n with T (0) = 0. (b) T (n) = T (n − 1) + cn with T (0) = 1, where c > 1 is some constant (c) T (n) = 2 T (n − 1) + 1 with T (

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Let f(n) y g(n) two positive asymptotic functions. Prove or disprove the following conjectures: a) f(n) = O(g(n)) implies 2f(n) = O(29(n)). b) f(n) = O(g(n)) implies g(n) = N(f(n)). c) g(n) = O((g(n))²).

Prove or Disprove: For all real valued functions f, if f(n) is O(2¹), then f(2m) is 0(2m).

Give the solution for T(n) in each of the following recurrences. Assume that T(n) is constant for small n. Provide brief justification for your answers.

Given the following recurrence, find the growth rate of T(n):T(n) = 4T(n/2) + 6n3 with T(1) = Θ(1)

N.png ... If gcd(a, m) = 1, then the unique solution xo to ax = b (mod m) is equal to (1) xo = ab (mod m) (2) xo = ab (mod m), where b is the inverse of b. (3) xo = ām (mod m), where ā is the inverse of a. (4) xo = āb (mod m), where ā is the inverse of a. A Choice (2) (B) Choice (1) Choice (4) (D) Choice (3)

Let T(n) be defined by the first-order linear recurrence T(n) = 2T(n-1) +8 Suppose it is given that T(2) = c. Compute T(0) by iterating backwards and express your answer in terms of c. T(0) =

Show that the solution of T(n) = T(n-1) + n is O(n^2). Do not use the Master Theorem.