Re: A curious result?
- To: mathgroup at smc.vnet.net
- Subject: [mg91512] Re: [mg91488] A curious result?
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Sun, 24 Aug 2008 07:08:14 -0400 (EDT)
- Reply-to: hanlonr at cox.net
Integrate[1/n^(1 + x), {n, 1, Infinity}, Assumptions -> {x > 0}]
1/x
Sum[1/n^(1 + x), {n, 1, Infinity}]
Zeta[x + 1]
Series[Zeta[x + 1], {x, 0, 1}] // Normal
(-StieltjesGamma[1])*x + EulerGamma + 1/x
% // N
0.07281584548367673*x + 0.5772156649015329 + 1/x
Plot[Zeta[x + 1] - 1/x, {x, 0, 0.1}]
Bob Hanlon
---- amzoti <amzoti at gmail.com> wrote:
=============
a. Sum[1/n^1.001, {n, 1 , Infinity}] = 1000.58
b. Integrate[1/n^(1.001), {n, 1, Infinity}] = 1000