## LaTex and solution for an infinite series

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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 Quote by Loren Booda 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: $$1-2^{-1/2}+3^{-1/2}-4^{-1/2}+...=1-\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}-\frac{1}{\sqrt{4}}+...=\sum_{n=1}^\infty\frac{(-1)^{n-1}}{\sqrt{n}}$$

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

DonAntonio
 Blog Entries: 8 Recognitions: Gold Member Science Advisor Staff Emeritus A LaTeX guide is here: http://www.physicsforums.com/showthread.php?t=546968