I've got to transform [2;1,5] with the 5 being the only repeated number into a fraction. I know the answer is (23+sqrt(29))/10 but how do I get from the question to the answer. If somebody could guide me through slowly I'd be very grateful as I'm really struggling. It is the only part of continued fractions I don't get.
Sorry I screwed up the posting last time
2007-01-22 13:52:13 · 3 answers · asked by kewlguitarist 2 in Science & Mathematics ➔ Mathematics
Hmmm... I do not think this is exactly what you are looking for, but I can make (23+sqrt(29))/10 with 1,2,5.
Notice that if x = 1/(5 + (1/(5 + ...))) then x = 1/(5+x) so
x^2 + 5x -1 = 0 so x = (-5 + sqrt(29))/2
Then x/5 = (-5 + sqrt)/10
So (5 + 5 + 5 - 1 + x)/5 =
(5 + 5 + 5 - 1 + 1/(5 + (1/(5 + ...))))/5
= (23+sqrt(29))/10
So I made (23+sqrt(29))/10 with just 1's and 5's, but I am guessing that this is not exactly what you wanted. Hopefully it will help though.
Good luck!
2007-01-22 14:56:23 · answer #1 · answered by Phineas Bogg 6 · 0⤊ 0⤋
[2;1,5] <--- I don't know what this means.
As far as I can see it is 2 followed by a semicolon, the na 1 followed by a comma and then a 5. The 5 is said to be the only repeated number.
Somehow we are to convert [2;1,5] into a fraction.
All I can tell you is that .55555555555555555555 = 5/9.
2007-01-22 14:09:17 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋
2.1 is 2.5 is 10 so 29/10
2007-01-22 13:57:47 · answer #3 · answered by westsideballa_23 1 · 0⤊ 0⤋