Real sequence/Arithmetical mean/Dependent on start value/Convergence/Exercise
Let . For initial value , let a real sequence be recursively defined by
Show the following statements.
(a) For , we have for all , and the sequence is strictly decreasing.
(b) For , the sequence is constant.
(c) For , we have for all . and the sequence is strictly increasing.
(d) The sequence converges.
(e) The limit is .