Rise and Fall

Calculus Level 4

Suppose \(a > b > 0\) and \(a_1 =\dfrac{a+b}{2}\), \(b_1= \sqrt{ab}\). And for \(n \ge 2\), \(a_n \) and \(b_n\) are defined as \( \large a_n = \frac{1}{2}(a_{n-1} +b_{n-1}) \) and \( \large b_n = \sqrt{a_{n-1} b_{n-1}} \) respectively.

Then choose the right statement for the sequences \(a_n \) and \(b_n\).

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