10 Feb
2013
10 Feb
'13
1:58 p.m.
On 10/02/2013 13:59, Keith F. Lynch wrote:
The way I figured it:
All numbers are divisible by 1, so add 1. Half the numbers are divisible by 2, so subtract 1/2. A third of the numbers are divisible by 3, so add 1/3. A fourth of the numbers are divisible by 4, so subtract 1/4. A fifth of the numbers are divisible by 5, so add 1/5. etc...
And it's well known that 1 - 1/2 + 1/3 - 1/4 + ... converges to the natural log of 2.
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. -- g