3 Jan
2012
3 Jan
'12
8:03 p.m.
On Wednesday 04 January 2012 01:17:49 Dan Asimov wrote:
A few years ago I read in some math journal that a certain sum of reciprocal integer powers has an unexpectedly simple sum -- I think it was 3/5.
But I can't find the article or a reference to this fact. So I don't know just which reciprocal integer powers are being summed (or whether 3/5 is right).
I don't think this is what you're after -- it's too easy and the sum isn't 3/5 or much like it -- but sum {n>=2,k>=2} 1/n^k = sum {n>=2} sum {k>=2} 1/n^k = sum {n>=2} 1/n(n-1) = sum {n>=2} 1/(n-1) - 1/n = 1 which is kinda cute. (Query: is there a "trivial" proof that regards each 1/n^k term as a probability or something and thereby makes it instantly obvious that the sum is 1?) -- g