5 ms·
That's right, this is the simplest way to show it.
That's right, this is the simplest way to show it.
Nope, there's an even simpler way.
Say f(x) is the expected value of the number of draws to get to value x.
Then f(x) = 1 + integral_0^x f(x)
Hence f'(x) = f(x), so f(x) = c exp(x)
The constant is of course 1, and f(1) = exp(1).