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From: hiyaho on 18 Apr 2010 17:09
make n\to 2n to find
\zeta(s)~\sum(1/n^s-1/(1+n)^s)=\sumf(2n)
R(s)=(-1,)
make derivation of series f
\sumln(n)/n^s-ln(n)/(1+n)^s
calculate the remainder out of the first n terms
~ln(n)/n^s+C
C at R(s)>0 is uniform finit
According to the popular opionion
sum of first n terms(n)+reminder(n)=C(s)
make R(s) close to 0 and make n close to infinity，controversy can be found.
Puzzle：
Sum of every term derivation f at R(s)>0 is finit？
Explaination：
Continue derivation depend on uniform convengence of the series，but in fact it's only absolutely convergent，The calulation's validity here depends on the presumption of contintue derivation of $zeta(s)$。

Tao used at R(s)>1-\delta the property of analytic，

Criticism is welcomed！
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