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

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# sum of the series $\sum_{n=1}^\infty \frac{(-1)^{(n-1)}}{\sqrt{n}}$?

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