Suppose that d1, d2, d3,... is a sequence defined as follows: d1 = 9 10 , d2 = 10 11

Chapter 5, Problem 4

(choose chapter or problem)

Suppose that \(d_{1}, d_{2}, d_{3}\), . . . is a sequence defined as follows:

\(d_{1} = \frac {9}{10}, d_{2} = \frac {10}{11}\),

\(d_{k} = d_{k−1} \cdot d_{k−2}\) for all integers k ≥ 3.

Prove that \(0 < d_{n} ≤ 1\) for all integers n ≥ 0.

Text Transcription:

d_1, d_2, d_3

d_1 = 9 / 10, d_2 = 10 / 11

d_k = d_k−1 cdot d_k−2

0 < d_n ≤ 1