Define a sequence from R as follows. Fix r > 1. Let a1 = 1
and...
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Define a sequence from R as follows. Fix r > 1. Let a1 = 1and define recursively, an+1 = (1/r) (an + r + 1). Show, byinduction, that (an) is increasing and bounded above by (r+1)/(r?1). Does the sequence converge?
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MonotoneConvergence Theorem A monotone sequence of real numbers isconvergent if and only if it is boundedTheorem If a
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