Exam-Style Problem
⬅ Back to Subchapter
Browsing as Guest. Progress, bookmarks and attempts are disabled.
Log in to track your work.
FM June 2022 p12 q03
4234
The sequence of positive numbers \(u_1, u_2, u_3, \ldots\) is such that \(u_1 > 4\) and, for \(n \geq 1\),
\(u_{n+1} = \frac{u_n^2 + u_n + 12}{2u_n}.\)
(a) By considering \(u_{n+1} - 4\), or otherwise, prove by mathematical induction that \(u_n > 4\) for all positive integers \(n\). [5]
(b) Show that \(u_{n+1} < u_n\) for \(n \geq 1\). [3]
Log in to record attempts.