LaTex and solution for an infinite series

[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.

 

[DonAntonio]

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

 

[micromass]

A LaTeX guide is here: https://www.physicsforums.com/showthread.php?t=546968

 

[Xitami]

http://en.wikipedia.org/wiki/Dirichlet_eta_function