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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




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