Define a sequence a_{0}a_{1 }a_{2}. . . recursively by setting a_{0 }= 1 and a_{n+1}= 3 – 1/a_{n}for all n= 0, 1, 2, 3, . . . use induction to prove that 0 < a_{n}< a_{n + 1}< 3 for all n = 0, 1, 2, 3, . . .

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- Oct 25th 2012, 03:53 PM #1

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## I would really appreciate it if someone could please help me with this question.

Define a sequence a

_{0}a_{1 }a_{2}. . . recursively by setting a_{0 }= 1 and a_{n+1}= 3 – 1/a_{n}for all n= 0, 1, 2, 3, . . . use induction to prove that 0 < a_{n}< a_{n + 1}< 3 for all n = 0, 1, 2, 3, . . .

- Oct 25th 2012, 05:34 PM #2

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- Oct 25th 2012, 06:09 PM #3

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## Re: I would really appreciate it if someone could please help me with this question.

hey thanks alot. but i am still having a bit of difficulties with the -a^2(subscript n). i understand that the [3a(subscript n) -1]/a(subscript n) came from the a(subscript n+1) but i don't understand how -a(subscript n) gives u that -a^2(subscript n)

- Oct 26th 2012, 03:52 AM #4

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