Clarence
  • Clarence
What is this question asking me to do? Assuming that the sequence {an} defined below is convergent, find its limit. a1=1,an+1=12−1an,n≥1.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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ganeshie8
  • ganeshie8
you need to find \(\lim\limits_{n\to\infty}~a_n\)
Clarence
  • Clarence
\[a _{1}=1,a _{n+1}=12-\frac{ 1 }{ a _{n} }, n \ge1\]
Clarence
  • Clarence
How would I go abouts doing that? @ganeshie8

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ganeshie8
  • ganeshie8
use below \(\lim\limits_{n\to\infty}~a_{n+1} = \lim\limits_{n\to\infty}~a_n\)
ganeshie8
  • ganeshie8
let \(\lim\limits_{n\to\infty}~a_n =\lim\limits_{n\to\infty}~a_{n+1} =x\)
ganeshie8
  • ganeshie8
so you want to solve \(x\)
ganeshie8
  • ganeshie8
we have \(a _{n+1}=12-\frac{ 1 }{ a _{n} }\) take limit \(\lim\limits_{n\to\infty} a _{n+1}=\lim\limits_{n\to\infty} 12-\frac{ 1 }{ a _{n} }\\~\\x = 12-\frac{1}{x}\) you can solve \(x\)
Clarence
  • Clarence
\[x=6\pm \sqrt{35}\] But how did you manage to get that from the question?
ganeshie8
  • ganeshie8
get what ?
Clarence
  • Clarence
Get what to do :p
ganeshie8
  • ganeshie8
ahh i have already told you :) you need to be a lil more specific haha
Clarence
  • Clarence
How did you know that you had to equate the two limits together to figure out the question and stuff? :P
ganeshie8
  • ganeshie8
okay honestly i didn't invent that trick... i don't think its some thing that occurs easily to anyone... it needs to be shown by others...
Clarence
  • Clarence
Ahh, fair enough then, well thanks for the assistance as always! :)
ganeshie8
  • ganeshie8
np :)

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