Consider the following recurrence relation, give the Big-Theta behaviour of T(n) using induction:

Solve the first-order linear recurrence relation: Sn+1 = 5 Sn + 1, with S0=1. You may use the general solution given on P.342.

Question 4: Consider two recurrence relations P(n) = 2P(n/2) +n and Q(n) = 4Q (n/4) +2n. What is the relationship between P and Q? Is P = O(Q), P = N(Q), or P = O(Q)? Prove your answer using limit of ratio definition of asymptotic notations.

Consider the following recurrence relations: А. ТА(п) 2× TA(꽃) +n B. Tp(n) = 4 × Tâ() +n² C. Tc(n) = 8 × Tc()+n D. Tp(n) =8×Tp(플) + 1 and T4(1) = TB(1) = Tc(1) = Tp(1) = 0(1) || Problem: Assuming that each node in their respective recursion trees consume the same amount of constant space, which recurrence relation/s has/have the worst worst- case space complexity (O(M(n)))? Would this/these also require the most amount of space or program stack memory?

Solve this recurrence relations together with the initialconditions given. a_{n+2} = −4a_{n+1} + 5a_n for n ≥ 0, a_0 = 2, a_1 = 8

Asymtotic Analysis : Prove the following claims

Question 1) . Apply Master Theorem to bound each one of the following recurrence relations using Big-O notation. Show all your work. In all cases T(n)=1. a) T(n)= 4T(n/4) + 12 n4 b) T(n)= T(n/2) + log n c) T(n)= 2 T(n/2) + 57 n3 d) T(n)= 3 T(n/2) + O(n)

Simplify n∧(¬q∨q) to n

Need help with in-depth step-by-step solving of the recurrence relations below using the Iterative Substitution method Fill in the blanks for closed-form expression, and the Big Theta. T(n) = {1,                            if n=1          { T(n/5)+5,               if  n > 1 Closed-form expression: Rate of growth :  For reference answers are :Closed-form expression: Answer -> 5log5n + 1Rate of growth: Answer -> Θ (log n)

Apply Master Theorem to bound each one of the following recurrence relations using Big-O notation. Please show work in depth. In all cases T(n)=1.