Consider the sequence defined by b1 = 1, b2 = 2, b3 = 3, bn+3 = bn+2 + bn+1 + bn. Show that for all positive integer n, bn < 2^n
Question
Solution 1
Step 1: Understanding the Problem We need to prove that for all positive integers n, the sequence bn defined by b1 = 1, b2 = 2, b3 = 3, bn+3 = bn+2 + bn+1 + bn, satisfies bn < 2^n.
Step 2: Base Case For n = 1, 2, 3, we have b1 = 1 < 2^1, b2 = 2 < 2^2, and b3 = 3 < 2^3. So, the statement holds for n Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
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