i need this immediatly,, please people!!!
2006-10-23 14:11:53 · 3 answers · asked by doomed_dream 1 in Science & Mathematics ➔ Mathematics
[2,4,4,4,4,...], in other words
2+1/(4+1/(4+1/(....
2006-10-23 14:44:07 · answer #1 · answered by mathematician 7 · 2⤊ 0⤋
Let â5 = 2 + 1 / x.
Then x = 1 / ( â5 - 2 ) = ( â5 + 2 ) / ( 5 - 4 ) = â5 + 2
Let â5 + 2 = 4 + 1 / y.
Then y = 1 / (â5 + 2 - 4 ) = 1 / (â5 - 2 ) = â5 + 2
= 4 + 1 / y
Repeating, and collecting
â5 = 2 + 1 / (4 + 1 / ( 4 + ( 1 / ( 4 +...
which is wriiten as the (simple) continued fraction
â5 = [ 2 , 4 , 4 , 4 , ... ]
2006-10-23 22:31:59 · answer #2 · answered by p_ne_np 3 · 0⤊ 0⤋
Check it out: Wikipedia has a link to a continued fraction generator. It will do sqrt(5)
http://wims.unice.fr/wims/wims.cgi?module=tool/number/contfrac.en
2006-10-23 21:25:12 · answer #3 · answered by modulo_function 7 · 1⤊ 1⤋