1 mathematics Q.

http://i1090.photobucket.com/albums/i376/Nelson_Yu/int-6.jpg

圖片參考：http://i1090.photobucket.com/albums/i376/Nelson_Yu/int-6.jpg


2011-09-03 10:37:39 補充：
Sorry a_(n+1) should be √13 + (√13 - 13) / (√13 + a_n)

2011-09-03 17:46:12 補充：
I have corrected already in 補充.
a_(n+1) should be √13 + (√13 - 13) / (√13 + a_n)

2011-09-03 18:07:36 補充：
differentiation is just a convenient way to evaluate error. If you cannot satisfy yourself with this, you may refer to the below file:
http://i1090.photobucket.com/albums/i376/Nelson_Yu/int-13.jpg

2011-09-03 18:08:10 補充：
This just yield the same error estimation as differentiation

2011-09-03 21:07:44 補充：
A simple way, use a value just bigger or smaller than one of the possible answers, then calculate the new result. If the new result goes further away from the value, then this value is not stable and should be discarded. If the new result comes closer, then it is the stable answer.

2011-09-03 21:13:16 補充：
In this case the 2 possible results are +-1.8988
Use a_n = -2 then a_(n+1) = -2.246 (away from -1.8988)
Use a_n = +2 then a_(n+1) = 1.930 (closer to 1.8988)
So 1.8988 is the correct answer

To 自由自在:

in the 2nd and 3rd line in your solution,
when you substitute a[n]=(13)^(1/4) into 2nd line,
a[n+1] wont equal to 13^(1/4)!!!!!!

2011-09-03 20:34:15 補充：
so, the method is to find the 3th,4th 'term', so that we can find out which value[(13)^(1/4) or (13)^(1/4)] will the expression go to . right?

To 自由自在:

Why can you apply differentiation on sequence?