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A sequence {an} is defined recursively by a1 = 2, a2 = 2 and an = an2an1 for n 3.(a)

Chapter 4, Problem 22

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QUESTION:

A sequence {an} is defined recursively by a1 = 2, a2 = 2 and an = an2an1 for n 3.(a) Determine an for 3 n 6.(b) Conjecture a formula for an for n 1.(c) Prove that the conjecture in (b) is correct.

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QUESTION:

A sequence {an} is defined recursively by a1 = 2, a2 = 2 and an = an2an1 for n 3.(a) Determine an for 3 n 6.(b) Conjecture a formula for an for n 1.(c) Prove that the conjecture in (b) is correct.

ANSWER:

Step 1 of 4

Finding  between

Substituting values n= 3,4,5,6 for   for

Given:

 

 

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