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Martin

Tue Oct 05, 2004 11:18 pm


Limit of a series

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Alright, I know how to find the limit of a sequence. A series, on the other hand, is providing me with an endless amount of trouble.

Here is my sequence: a(1) = 1, a(n+1) = 1 + 1/a(n)

Apparently it converges (has a sum). Also, apparently the limit of this sequence is root 2.

Now, can someone please explain to me how to do this?


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AsianSensation

Fri Oct 15, 2004 2:53 pm



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probably too late, but anyways.

a(n+1) = 1 + 1/a(n)

let Lim a(n+1), as n gets larger and larger be k.

take Limit of both sides.

Lim a(n+1) = Lim (1 + 1/a(n))

which becomes

K = 1 + 1/K
K^2 = K + 1
K^2 - K - 1 = 0
K = (1 + or - sqrt (1 + 4))/2
K = (1 + sqrt (5))/2

So, yeah, you sure it's root 2? I get Golden Ratio.......


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Andy

Sat Oct 16, 2004 1:36 pm



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azn, u solvoed for Lim a(n+1), he wanted to know the limit of the series.. not the sequence


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AsianSensation

Sat Oct 16, 2004 9:11 pm



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oh, series, my bad.

then I have not teh learn3d teh leet math way.


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Martin

Sun Oct 17, 2004 1:11 am



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Yeah, I tried the same thing :(

Ahh well. Thanks for the help though, those marks are long lost.