5
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Find the smallest integer $n$ such that $$\left(1-\frac{n}{365}\right)^n < \frac{1}{2}.$$

I cannot use a calculator, and I do not know where to begin.

  • 5
    Do you mean you are not allowed to use a calculator, or do you mean you don't know how to use a calculator, or do you mean you have no access to a calculator?2011-10-31
  • 0
    I am not allowed to use a calculator.2011-10-31
  • 0
    Are you familiar with the [binomial theorem](http://en.wikipedia.org/wiki/Binomial_theorem)?2011-10-31
  • 0
    you cannot find smallest integer,you can only find smallest positive integer which is $16$ by the way...2011-10-31

2 Answers 2