Suppose a sequence an, is defined as follows: a1 = 9/10, a2 = 10/11, an+2 = an+1an.Show that 0 < an < 1 for all (positive integers) n.

Question

Suppose a sequence an, is defined as follows: a1 = 9/10, a2 = 10/11, an+2 = an+1an.Show that 0 < an < 1 for all (positive integers) n.
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Solution 1

Step 1: Understanding the Problem We need to prove that for all positive integers n, the sequence an defined by a1 = 9/10, a2 = 10/11, an+2 = an+1an, satisfies 0 < an < 1.

Step 2: Base Case We can see that a1 = 9/10 and a2 = 10/11 are both between 0 and 1.

Step 3: Inductive Step Assume that for so 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.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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