Consider the following recurrence relation

Mathematics
Tutor: None Selected Time limit: 1 Day

May 23rd, 2015

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

                                         B (k -1) =  3k-1 - 1  for some k>1

Inductive Hypothesis: suppose.....

Inductive Step: Using...

B(k) = .......................

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

        = ( 3k - 3 ) +2

        = 3k - 1

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


 

 

May 23rd, 2015

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