Let a_{1} > 1, and suppose a_{n+1} = 2 - 1/a_{n} for all n >= 2 . Prove that (a_{n}) converges, and find its limit.
Last edited by Kanwar245; Mar 15th 2013 at 08:43 PM.
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Originally Posted by Kanwar245 Let a_{1} > 1, and suppose a_{n+1} = 2 - 1/a_{n} for all n >= 2 . Prove that (a_{n}) converges, and find its limit. It is sufficient to show that the sequence is decreasing and bounded below. Do that with induction. The solve the equation .
Don't you think there's a typo, since we are given a1 > 1, and a_n+1 is for n>= 2
Originally Posted by Kanwar245 Don't you think there's a typo, since we are given a1 > 1, and a_n+1 is for n>= 2 Why should anyone think that? Take a look at this
Last edited by Plato; Mar 15th 2013 at 04:46 PM.
Okay, so when proving through induction that it's monotonically decreasing, I just need to prove that a_{n+1} >= a_{n} right
Originally Posted by Kanwar245 Okay, so when proving through induction that it's monotonically decreasing, I just need to prove that a_{n+1} >= a_{n} right BASE CASE: Prove that . PROVE Inductive case: If then .
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