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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 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

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  1. anonymous
    • 5 years ago
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    f) Use parts (c) and (e) to show that the sequence has a limit.

  2. anonymous
    • 5 years ago
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    any ideas whatsoever?

  3. anonymous
    • 5 years ago
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    The second term...is strange..-nxn+1? Is that -xn^2+1?

  4. anonymous
    • 5 years ago
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    -nx^n+1

  5. anonymous
    • 5 years ago
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    -nx^(n+1) or -nx^(n) +1?

  6. anonymous
    • 5 years ago
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    -nx^(n+1)

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spraguer (Moderator)
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