Limit the mixed recurrence

Calculus Level 3

Let \(a_0 = 1, b_0 = 2,\) and for \(n\geq 0\) \[a_{n+1} = \frac{a_n + b_n}{2},\quad b_{n+1} = \sqrt{a_{n+1}b_n}.\] If \( \displaystyle \lim_{n\to\infty } a_n b_n = \dfrac c{\pi^ d} \) for positive integers \(c\) and \(d\), find \(c+d\).

×

Problem Loading...

Note Loading...

Set Loading...