Hi,

We know that the series $\sum_{n=1}^\infty \frac{(-1)^{(n-1)}}{\sqrt{n}}$ is convergent and it is oscillating. and numerically it is almost 0.6048986434.

I want to know what is the exact limit of this series and how we can find that analytically.

Now if we let $A(t):=\sum_{n=1}^t\frac{(-1)^{(n-1)}}{\sqrt{n}}$, is there any simple formula without summation that is equal to $A(t)$.