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 Oct 18, 2018
 #1
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If a(1)=1/(1 - x),  a(2)=1/(1 - a(1)), and a(n)=1/(1 - a(n) - 1), for n => 2, x does not=0, then find a(107) in simplest form.
thess: You could have made it a little smaller!!!. 

 Oct 18, 2018
 #2
avatar+27847 
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I think this should probably read as:

 

\(\text{if } a_1=\frac{1}{1-x},a_2=\frac{1}{1-a_1}, \text{ and }a_n=\frac{1}{1-a_{n-1}}\text{, for }n\ge2, x\ne0,\text{ find }a_{107}\text{ in simplest form}\)

Alan  Oct 18, 2018
 #3
avatar+27847 
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Try a few terms! 

 

a1=1/(1-x), a2=1/(1-a1)→1/(1-1/(1-x))→1-1/x, a3=1/(1-a2)→1/(1-(1-1/x))→x,

continuing in this fashion we find

a4=1/(1-x), a5=1-1/x, a6=x ...etc.

 

So a107=...

(I’m sure you can take it from here)

 Oct 18, 2018
edited by Alan  Oct 18, 2018

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