Question

Prove by strong induction that ?(base ?) =3^(?) −2^(?) for all ?≥0 .

Prove by strong induction that ?(base ?) =3^(?) −2^(?) for all ?≥0 .

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Answer #1

Let the induction hypothesis, a(n), be

Base Case: For n = 0,

and For n=1,

hence these true on both values of n = 0 and 1.

Inductive Step: Assume that and , where , are true for purposes of induction.

Then and

Since we assumed A(n−1) and A(n−2), we can We rewrite

thus, we get

its proved....

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