Bascule is reading a book.
What is the probability that the first digit of the page he is on is 1, 2, 3, 4 or 5?
a) obtain an expression
b) approximate a numerical value
(In reply to
well.. by Cheradenine)
> since the proportions are
> similar in all 10^x intervals, an expression
> in the form of a sum for these intervals will
> have a limit as x tends to ∞
>
> this reasoning implies that there exists
> a value between 0 and 1 which is the
> single correct answer to the question
> (probably between 0.8 and 0.9)
I'm going to have to disagree with this one as well. I don't think the quantity will ever converge. For each 10^x interval, there will be a fluctuation between 0.55 and 0.95 or somewhere thereabouts (I haven't worked out the actual numbers). Every octave exhibits this behavior. It's a bit like asking for the limit of sin x as x approaches ∞. It's a well-defined expression, but there is nevertheless no convergence.