10 Feb
2013
10 Feb
'13
5:08 p.m.
On 10/02/2013 21:02, Adam P. Goucher wrote: [Keith Lynch:]
And it's well known that 1 - 1/2 + 1/3 - 1/4 + ... converges to the natural log of 2.
[me:]
Oh, that's sooooo much simpler than what I did! And I bet it's possible to make it rigorous enough despite the fact that the series isn't absolutely convergent.
[Adam:]
Yes, just take the first n! terms, and let n tend to infinity.
Surely that proves only that there are *some* N such that the average over the first N years is log 2. (Hence, in particular, that if the limit exists then that's its value.) -- g