Recall that the Fibonacci and Lucas sequences Fn and Ln are (0, 1, 1, 2, . . . ) and (2, 1, 3, 4, . . .
), respectively. Given that x0 = x1 for the sequence xn in part (d), show that the ratio xn/(Fn +
Ln) does not depend on n.
where part (d) gives xn = xn?1 + xn?2 where n >= ?? 2.
Solution
Sequence in part (d) is given by (x0, x0, 2x0, 3x0, 5x0,8x0,....) = x0(1,1,2,3,5,8,....)
Fn + Ln = (2,2,4,6,10,....) = 2(1,1,2,3,5,8,....)
So clearly if we divide the nth term of xn and Fn+Ln then we get xn/(Fn+Ln) = x0/2 which does
not depend on n.
Recall that the Fibonacci and Lucas sequences Fn and Ln are (0, 1, 1.pdf
1. Recall that the Fibonacci and Lucas sequences Fn and Ln are (0, 1, 1, 2, . . . ) and (2, 1, 3, 4, . . .
), respectively. Given that x0 = x1 for the sequence xn in part (d), show that the ratio xn/(Fn +
Ln) does not depend on n.
where part (d) gives xn = xn?1 + xn?2 where n >= ?? 2.
Solution
Sequence in part (d) is given by (x0, x0, 2x0, 3x0, 5x0,8x0,....) = x0(1,1,2,3,5,8,....)
Fn + Ln = (2,2,4,6,10,....) = 2(1,1,2,3,5,8,....)
So clearly if we divide the nth term of xn and Fn+Ln then we get xn/(Fn+Ln) = x0/2 which does
not depend on n
