## anonymous one year ago 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.

1. ganeshie8

you need to find $$\lim\limits_{n\to\infty}~a_n$$

2. anonymous

$a _{1}=1,a _{n+1}=12-\frac{ 1 }{ a _{n} }, n \ge1$

3. anonymous

How would I go abouts doing that? @ganeshie8

4. ganeshie8

use below $$\lim\limits_{n\to\infty}~a_{n+1} = \lim\limits_{n\to\infty}~a_n$$

5. ganeshie8

let $$\lim\limits_{n\to\infty}~a_n =\lim\limits_{n\to\infty}~a_{n+1} =x$$

6. ganeshie8

so you want to solve $$x$$

7. 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 $$x$$

8. anonymous

$x=6\pm \sqrt{35}$ But how did you manage to get that from the question?

9. ganeshie8

get what ?

10. anonymous

Get what to do :p

11. ganeshie8

ahh i have already told you :) you need to be a lil more specific haha

12. anonymous

How did you know that you had to equate the two limits together to figure out the question and stuff? :P

13. 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...

14. anonymous

Ahh, fair enough then, well thanks for the assistance as always! :)

15. ganeshie8

np :)