# LaTex and solution for an infinite series

1. Jun 3, 2012

### 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.

2. Jun 3, 2012

### DonAntonio

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

3. Jun 4, 2012

4. Jun 5, 2012