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## Homework Statement

[itex]\sum[/itex] from n=1 to n=[itex]\infty[/itex] (1 + [itex]\frac{x}{n}[/itex])

^{n2}

Determine the values of x for which the series converges absolutely, converges conditionally and diverges.

## The Attempt at a Solution

So i tried using the root test for the absolute value of (1 + [itex]\frac{x}{n}[/itex])

^{n2}, but it was inconclusive.

So then I tried using the ratio test, but I need to simplify this:

|1 + [itex]\frac{x}{n+1}[/itex]|

^{(n+1)2}/ |1 + [itex]\frac{x}{n}[/itex]|

^{n2}

and I have no idea how to simplify this.

I don't know any other tests that we could use for this, so I'm just pretty stumped.

Any help would be great.