MathGroup Archive 2008

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: A curious result?


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




  • Prev by Date: Extending running memory of Mathematica
  • Next by Date: RE: A curious result?
  • Previous by thread: RE: A curious result?
  • Next by thread: Re: A curious result?