Show mathematical work.So you would have 1, x, 1 + x,
1+ 2x,1+3x...form
2006-11-06 08:51:35 · 2 answers · asked by ttybrs10 1 in Science & Mathematics ➔ Mathematics
The x value will be (sqrt(5) - 1) / 2, or -.618, which is 1 - phi = -1 / phi, where phi is the golden ratio. If f_n is a fibonacci number, the ratio of f_n/f_(n+1) approaches phi - 1 as n approaches infinity. Since the terms of your sequence are of the form f_n + f_(n+1)*x, they would approach f_n + f_(n+1)*(-f_n/f_(n+1)) = f_n - f_n = 0, a convergence.
2006-11-13 05:21:12 · answer #1 · answered by DavidK93 7 · 0⤊ 0⤋
Sorry, but I don't think there is one that starts with 1 and is bounded.
In addition, your pattern is worng. For it to be Fibonacci "type", it would be
1, x, 1+x, 1+2x, 2+3x, 3+5x, and so on. That's why it's not bounded.
2006-11-06 17:32:16 · answer #2 · answered by Melody 3 · 0⤊ 0⤋