Answered: "Observe that the values of h(n) seem…

"Observe that the values of h(n) seem to be related to powers of 3" In what way are 2, 5, 14, and 41 related to 1, 3, 9, 27, 81, ...?

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Question

Thank you for your response.

In step 1, it is stated:

"Observe that the values of h(n) seem to be related to powers of 3"

In what way are 2, 5, 14, and 41 related to 1, 3, 9, 27, 81, ...?

I'm not seeing any relation here. Please explain.

Also, I'm not following the inductive step. I don't know where the 3 * h(k) - 1 came from or how the -2 changed to -1. There seem to be several steps not shown, and I don't understand how 3^(k+1) - 2 - 5 relates to anything. It doesn't compare to anything else that I can see expressed.

Thanks, again, for the help with this.

Expert Solution

Step 1: Consider the given data

h(n) = {1 if n = 1; 3 × h(n - 1) - 1 otherwise}

We need to express this in polynomial/xponential function of n.

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