Consider the sequence defined byb1 = 1, b2 = 2, b3 = 3, bn+3 = bn+2 + bn+1 + bn.Show that for all positive integer n, bn < 2n.

Question

Consider the sequence defined byb1 = 1, b2 = 2, b3 = 3, bn+3 = bn+2 + bn+1 + bn.Show that for all positive integer n, bn < 2n.
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Solution 1

To prove this, we can use the concept of mathematical induction.

Step 1: Base Case We start with the smallest values of n. For n=1, b1 = 1 which is less than 2^1 = 2. For n=2, b2 = 2 which is less than 2^2 = 4. For n=3, b3 = 3 which is less than 2^3 = 8. So, the statement holds for n=1, n=2, and n= Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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