• anonymous
We show that the sequence converges; its limit can be used to define e. (a) For a fixed integer n > 0, let f (x) = (n + 1)xn -nxn+1. For x > 1, show f is decreasing and that f (x) < 1. Hence, for x > 1. (b) Substitute the following x-value into the inequality from part (a) and show that (c) Use the inequality from part (b) to show that sn < sn+1 for all n > 0. Conclude the sequence is increasing. (d) Substitute x = 1 + 1/2n into the inequality from part (a) to show that (e) Use the inequality from part (d) to show s2n < 4. Conclude the sequence is bounded. (f) U
Mathematics
• Stacey Warren - Expert brainly.com
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