Given-sequence-x-n-with-0-lt-a-x-1-lt-x-2-b-x-n-1-x-n-1-x-n-n-1-2-3-review-sequence-r-n-with-r-n-x-n-1-x-n-n-1-2-3-a-Prove-that-1-lt-r-n-lt-2-for-n-2-3-4-b-

Question Number 31705 by gunawan last updated on 12/Mar/18

Given sequence (x_{n}) with 0 < a = x_{1} < x_{2} = b

x_{n + 1} = x_{n + 1} + x_{n}, n = 1, 2, 3, \dots

review sequence (r_{n}) with r_{n} = \frac{x_{n + 1}}{x_{n}}, n = 1, 2, 3, \dots

a . Prove that 1 < r_{n} < 2 for n = 2, 3, 4, \dots

b . Diverge or converge is the squence ?