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anonymous
 5 years ago
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 xvalue 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
anonymous
 5 years ago
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 xvalue 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

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0f) Use parts (c) and (e) to show that the sequence has a limit.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0any ideas whatsoever?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The second term...is strange..nxn+1? Is that xn^2+1?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0nx^(n+1) or nx^(n) +1?
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