need help with the 2 boxes with x mark Consider the following recurrence relation:=C(n) =) = {0+3. C(n-1) ifn>0.Prove by induction that C(n) = 3+1 -2n-3 for all n ≥ 0.4(Induction on n.) Let f(n) = 3n+1 - 2n-Base Case: If n = 0, the recurrence relation says that C(0) = 0, and the formula says that f(0) ==k+ 3.1Inductive Hypothesis: Suppose as inductive hypothesis that C(k-1)=f(k-1)AKInductive Step: Using the recurrence relation,C(k)=k+ 3 C(k-1), by the second part of the recurrence relation-33+1-6k-343−1+1 -2(k-1) – 3443k+1-2k-34Xby inductive hypothesisX0+1for some k > 0.4-2.0-30✓, so they match.

Recurrence Relation: A recurrence relation is an equation with rules that represents a…

Consider the following recurrence relation: if n = 0 if n > 0. C(n) = - {1+3.0 (n+3·C(n-1) Prove by induction that C(n) = 3n+1-2n - 3 for all n ≥ 0. 4 3n+1 - 2n (Induction on n.) Let f(n) = Base Case: If n = 0, the recurrence relation says that C(0) = 0, and the formula says that f(0) = Inductive Hypothesis: Suppose as inductive hypothesis that C(k-1) = f(k-1) =k+ 3. Inductive Step: Using the recurrence relation, C(K) = k + 3. C(k-1), by the second part of the recurrence relation 3-1+1-2(k-1)-3 4 3²+1 -3 4 -6k-3 4 X 4 3+1-2k-3 by inductive hypothesis X 0+1 for some k > 0. - 2.0 0 ✓ , so they match.

Consider the following recurrence relation: if n = 0 if n > 0. C(n) = - {1+3.0 (n+3·C(n-1) Prove by induction that C(n) = 3n+1-2n - 3 for all n ≥ 0. 4 3n+1 - 2n (Induction on n.) Let f(n) = Base Case: If n = 0, the recurrence relation says that C(0) = 0, and the formula says that f(0) = Inductive Hypothesis: Suppose as inductive hypothesis that C(k-1) = f(k-1) =k+ 3. Inductive Step: Using the recurrence relation, C(K) = k + 3. C(k-1), by the second part of the recurrence relation 3-1+1-2(k-1)-3 4 3²+1 -3 4 -6k-3 4 X 4 3+1-2k-3 by inductive hypothesis X 0+1 for some k > 0. - 2.0 0 ✓ , so they match.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter17: Markov Chains

Section17.5: Steady-state Probabilities And Mean First Passage Times

Problem 12P

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