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LaTex and solution for an infinite series

  1. Jun 3, 2012 #1
    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.
     
  2. jcsd
  3. Jun 3, 2012 #2
    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
     
  4. Jun 4, 2012 #3

    micromass

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  5. Jun 5, 2012 #4
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