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mathmath333

  • one year ago

How to quickly calculate 5!/e

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \text{ How to quickly calculate}\hspace{.33em}\\~\\ & \lfloor{\dfrac{5!}{e}\rfloor} \hspace{.33em}\\~\\ \end{align}}\)

  2. mathmath333
    • one year ago
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    by hand

  3. mathmate
    • one year ago
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    Do you mean pen and paper or mentally?

  4. mathmath333
    • one year ago
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    by pen and paper (hand)

  5. mathmate
    • one year ago
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    So would that not be 120/2.718281828?

  6. mathmath333
    • one year ago
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    yes

  7. mathmate
    • one year ago
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    Or you can do a quick mental approximation by 120/2.7=40/0.9=44.4

  8. mathmate
    • one year ago
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    If you want to refine it, subtract 2/300 of the calculated value (mentally if you want) to get 44.15 Accurate value is 44.14553294057308

  9. mathmath333
    • one year ago
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    it should be correct

  10. mathmate
    • one year ago
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    Interesting problem. Will be back.

  11. mathmath333
    • one year ago
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    ur thinking is correct of \(\approx n/2.7\)

  12. anonymous
    • one year ago
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    trying to learn derangements? :)

  13. mathmate
    • one year ago
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    As long as it is between 44 and 45, the floor function will convert it to 44. We need additional accuracy to get the lower bound so it doesn't go below 44.

  14. mathmath333
    • one year ago
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    nice forecasting of dearrangments.

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