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Define the function f...

Define the function f : N → N as follows.

f(n) =<:

f(n) =1 if n = 1

f(n) =5 if n = 2

f(n) =f(n − 1) + 2f(n − 2) if n ≥ 3

Prove that f(n) = 2n + (−1)n for all integers n ≥ 1.

f(n) =<:

f(n) =1 if n = 1

f(n) =5 if n = 2

f(n) =f(n − 1) + 2f(n − 2) if n ≥ 3

Prove that f(n) = 2n + (−1)n for all integers n ≥ 1.

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