LaTex and solution for an infinite series

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Discussion Overview

The discussion revolves around the representation of an infinite series using LaTeX, specifically the series 1-2-1/2+3-1/2-4-1/2+5-1/2... Participants also explore whether this series converges.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant requests the LaTeX representation and convergence status of the series 1-2-1/2+3-1/2-4-1/2+5-1/2...
  • Another participant provides a LaTeX representation of the series as 1-2^{-1/2}+3^{-1/2}-4^{-1/2}+5^{-1/2}+... and states it can be expressed as the sum ∑_{n=1}^∞ (-1)^{n-1}/√n.
  • This second participant claims that the series converges, citing it as an alternating Leibniz series with a general term sequence that converges monotonically to zero.
  • A third post shares a link to a LaTeX guide, suggesting resources for those unfamiliar with LaTeX.
  • A fourth post provides a link to the Dirichlet eta function, possibly as a related mathematical concept.

Areas of Agreement / Disagreement

There is a claim regarding the convergence of the series, but no consensus is reached among all participants about the convergence status or the implications of the series. The discussion includes multiple viewpoints on the representation and convergence.

Contextual Notes

The discussion does not clarify the assumptions regarding convergence criteria or the definitions of terms used in the series. The mathematical steps leading to the convergence claim are not fully resolved.

Loren Booda
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What is the LaTex and infinite sum for 1-2-1/2+3-1/2-4-1/2+5-1/2 . . .

Does it converge anyway?

I am too old for this to be a school assignment.
 
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Loren Booda said:
What is the LaTex and infinite sum for 1-2-1/2+3-1/2-4-1/2+5-1/2 . . .

Does it converge anyway?

I am too old for this to be a school assignment.

A PF contributor that doesn't know LaTeX? Strange...anyway: [tex]1-2^{-1/2}+3^{-1/2}-4^{-1/2}+...=1-\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}-\frac{1}{\sqrt{4}}+...=\sum_{n=1}^\infty\frac{(-1)^{n-1}}{\sqrt{n}}[/tex]

The sum converges as it is an alternating Leibnitz series: the general term sequence converges monotonically to zero and we have alternating signs.

DonAntonio
 

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