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.

Printable View

- March 15th 2013, 04:13 PMKanwar245Sequence convergence problem
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. - March 15th 2013, 04:33 PMPlatoRe: Sequences convergence problem
- March 15th 2013, 04:36 PMKanwar245Re: Sequences convergence problem
Don't you think there's a typo, since we are given a1 > 1, and a_n+1 is for n>= 2

- March 15th 2013, 04:40 PMPlatoRe: Sequences convergence problem
Why should anyone think that?

Take a look at this - March 15th 2013, 04:47 PMKanwar245Re: Sequences convergence problem
Okay, so when proving through induction that it's monotonically decreasing, I just need to prove that a

_{n+1}>= a_{n}right - March 15th 2013, 05:12 PMPlatoRe: Sequences convergence problem