Question

Consider a sequence defined recursively as X0= 1,X1= 3, and Xn=Xn-1+ 3Xn-2 for n ≥ 2....

Consider a sequence defined recursively as X0= 1,X1= 3, and Xn=Xn-1+ 3Xn-2 for n ≥ 2. Prove that Xn=O(2.4^n) and Xn = Ω(2.3^n).

Hint:First, prove by induction that 1/2*(2.3^n) ≤ Xn ≤ 2.8^n for all n ≥ 0

Find claim, base case and inductive step. Please show step and explain all work and details

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Answer #1

Any doubt in any step then comment below...i will explain you okk..

In solution i use Tn in place of Xn...so dont be confuse , both are same ..ok....

I prove that relation one by one , okk...

Base step is for n= 9 ..

And then we assume that result is true for any general step n= k ..and then by using this we have to prove that result is true for n= k+1 .. this is inductive step...

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