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moneybird

Find the non-negative number of c.

  • 2 years ago
  • 2 years ago

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  1. moneybird
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    \[f(n) = (1 - \frac{1}{2})(1 - \frac{1}{2^{2}})(1 - \frac{1}{2^{3}}) ... ((1 - \frac{1}{2^{n}})\] Find and prove a non-negative number "c" such that f(n) > c for all n

    • 2 years ago
  2. moneybird
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    c cannot be the largest c that will work, nor anywhere near it.

    • 2 years ago
  3. slaaibak
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    What do you mean by c cannot be the largest c that will work, nor anywhere near it ? If we compute the product like this: http://www.wolframalpha.com/input/?i=product+from+1+to+infinity+of+%281-1%2F2^%28n%29%29 we see it "converges" to: 0.288788095086602421278899721929 so if we must choose a c value, it can be anywhere between 0 and 0.288788095086602421278899721929 Or am I misreading things?

    • 2 years ago
  4. moneybird
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    The question was given that P(n) is always greater than 0.288. I am not really sure either

    • 2 years ago
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