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A sequence {an} is defined recursively by a1 = 2, a2 = 6 and an = 2an1an2 +2 for n

Chapter 4, Problem 21

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QUESTION:

A sequence {an} is defined recursively by a1 = 2, a2 = 6 and an = 2an1an2 +2 for n 3.Prove that an = n(n + 1) for every positive integer n.

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QUESTION:

A sequence {an} is defined recursively by a1 = 2, a2 = 6 and an = 2an1an2 +2 for n 3.Prove that an = n(n + 1) for every positive integer n.

ANSWER:

Step 1 of 3

The statement given in the question can be proved true using the mathematical induction. Using mathematical induction, the statement is assumed to be true for the value k and then proved to be true for k plus 1.

 

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