View the step-by-step solution to:

Thanks in advance.

I need help seeing the work done for this problem in my workbook, so that I can know how to do these on my own in the future. Thanks in advance. You all just take the money and deny questions to be answered. Please allow the tutor to begin the problem or even work an example with different variables so that I can know how to begin and end the problem!!!!!!!!!!!!!!!!!!!!!!!!!!

Consider the following recurrence relation.

B(n) = 2 if n=1

B(n)= 3*B(n − 1) + 2  if n > 1

Use induction to prove that B(n) = 3n − 1.

(Induction on n.) Let f(n) = 3n − 1.

Base Case: If n = 1,

 the recurrence relation says that B(1) = 2,

 and the formula says that f(1) = 3 − 1 =  ,

 so they match.

Inductive Hypothesis: Suppose as inductive hypothesis that B(k − 1) =  

 for some k > 1.

Inductive Step: Using the recurrence relation,

B(k) = 3 · B(k − 1) + 2, by the second part of the recurrence relation

 = 3    + 2, by inductive hypothesis

 = (3k − 3) + 2


so, by induction, B(n) = f(n)

 for all n ≥ 1.

Top Answer

This problem can be solve... View the full answer

Sign up to view the full answer

Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.


Educational Resources
  • -

    Study Documents

    Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

    Browse Documents
  • -

    Question & Answers

    Get one-on-one homework help from our expert tutors—available online 24/7. Ask your own questions or browse existing Q&A threads. Satisfaction guaranteed!

    Ask a Question
Ask a homework question - tutors are online