Let $n\in\mathbb N$. For$$e^xf_n(x)=\sum_{k=1}^\infty\frac{k^nx^k}{\left(k-1\right)!}$$show that $f_n(x)$ is a polynomial of degree $n+1$ with integer coefficients.

Tricky question.

Question

Let $n\in\mathbb N$. For$$e^xf_n(x)=\sum_{k=1}^\infty\frac{k^nx^k}{\left(k-1\right)!}$$show that $f_n(x)$ is a polynomial of degree $n+1$ with integer coefficients.

Tricky question.

anonymous · Answer

@TuringTest @KingGeorge @Zarkon You guys might be interest.

anonymous · Answer

@bahrom7893 You too, maybe lol.

turingtest · Answer

I got a linear thingy when I tried it that makes no sense, I'll write my work in a minute just so somebody can laugh at it

bahrom7893 · Answer

no im most likely not interested lol

bahrom7893 · Answer

Anyway... I'm off for tonight guys, interviews in 10 hrs. I need my sleep. Gnite eastern front.

anonymous · Answer

Cheers, good luck. Don't dead.

bahrom7893 · Answer

thanks :)

perl · Answer

what is f sub n (x) ?

anonymous · Answer

You can ignore the sub. It's just a marker to show that the function $f$ is dependent on $n$.

perl · Answer

well first lets look at e^x, whats the series of this

anonymous · Answer

You don't have to walk me through it, lol, I already have the solution. This is just a very difficult challenge.

perl · Answer

e^x |dw:1348817638823:dw|