What does $\sum_{n\in\mathbb N}\frac{n^x}{x^n}$ converge to when $x\in\mathbb R^+$ and $x1$?

Question

What does $\sum_{n\in\mathbb N}\frac{n^x}{x^n}$ converge to when $x\in\mathbb R^+$ and $x>1$?

anonymous · Answer

$\sum_{n\in\mathbb N}\frac{n^x}{x^n}$

anonymous · Answer

Yes, I forget this isn't M.SE. :)

anonymous · Answer

just so i can read it, i don't know it

anonymous · Answer

i think if you use \[ instead of \( it will work

anonymous · Answer

I fixed it, refresh. The "\(" is for inline equations.

anonymous · Answer

aah now i can see it
dollar signs don't work here for some reason

anonymous · Answer

I'm just trying to make sure this question is M.SE material before I post it, aha. Maybe it has a trivial solution I'm missing.

anonymous · Answer

is it supposed to be something nice?

anonymous · Answer

Not sure.

jhannybean · Answer

It's so tiny I can'r even read it.

jhannybean · Answer

$$\huge \sum_{n\in\mathbb N}\frac{n^x}{x^n}$$

jhannybean · Answer

@satellite73 I'm not sure what $\large n \in \mathbb N$ means :|

anonymous · Answer

$n$ is natural. $x$ is positive reals.

jhannybean · Answer

So basically to infinity....yes ?

anonymous · Answer

Yes.

jhannybean · Answer

Ohh ok. Just to make sure... $$\large \sum_{n=1}^{\infty} \frac{n^x}{x^n}$$Yeah im not sure if n would start at 0 or1....

jhannybean · Answer

@mathstudent55  ? :\

anonymous · Answer

n starts at 1.

dan815 · Answer

n E N just means n is all natural numbers

dan815 · Answer

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