Base case: If n = 1, the recurrence relation says.......that f(1) = 3^ 1 - 1 = 2, so they match.

B (k -1) = 3^{k-1 }- 1 for some k>1

Inductive Hypothesis: suppose.....

Inductive Step: Using...

B(k) = .......................

= 3( 3^{k-1 }- 1 ) + 2, by inductive hypothesis

= ( 3^{k} - 3 ) +2

= 3^{k }- 1

so, by induction, B(n) = f(n) for all n>1.

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