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badreferences
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Let \(n\in\mathbb N\). For\[e^xf_n(x)=\sum_{k=1}^\infty\frac{k^nx^k}{\left(k1\right)!}\]show that \(f_n(x)\) is a polynomial of degree \(n+1\) with integer coefficients.
Tricky question.
 2 years ago
 2 years ago
badreferences Group Title
Let \(n\in\mathbb N\). For\[e^xf_n(x)=\sum_{k=1}^\infty\frac{k^nx^k}{\left(k1\right)!}\]show that \(f_n(x)\) is a polynomial of degree \(n+1\) with integer coefficients. Tricky question.
 2 years ago
 2 years ago

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badreferences Group TitleBest ResponseYou've already chosen the best response.1
@TuringTest @KingGeorge @Zarkon You guys might be interest.
 2 years ago

badreferences Group TitleBest ResponseYou've already chosen the best response.1
@bahrom7893 You too, maybe lol.
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
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
 2 years ago

bahrom7893 Group TitleBest ResponseYou've already chosen the best response.0
no im most likely not interested lol
 2 years ago

bahrom7893 Group TitleBest ResponseYou've already chosen the best response.0
Anyway... I'm off for tonight guys, interviews in 10 hrs. I need my sleep. Gnite eastern front.
 2 years ago

badreferences Group TitleBest ResponseYou've already chosen the best response.1
Cheers, good luck. Don't dead.
 2 years ago

bahrom7893 Group TitleBest ResponseYou've already chosen the best response.0
thanks :)
 2 years ago

perl Group TitleBest ResponseYou've already chosen the best response.0
what is f sub n (x) ?
 2 years ago

badreferences Group TitleBest ResponseYou've already chosen the best response.1
You can ignore the sub. It's just a marker to show that the function \(f\) is dependent on \(n\).
 2 years ago

perl Group TitleBest ResponseYou've already chosen the best response.0
well first lets look at e^x, whats the series of this
 2 years ago

badreferences Group TitleBest ResponseYou've already chosen the best response.1
You don't have to walk me through it, lol, I already have the solution. This is just a very difficult challenge.
 2 years ago

perl Group TitleBest ResponseYou've already chosen the best response.0
e^x dw:1348817638823:dw
 2 years ago

perl Group TitleBest ResponseYou've already chosen the best response.0
so we can see immediately that
 2 years ago

perl Group TitleBest ResponseYou've already chosen the best response.0
dw:1348817750800:dw
 2 years ago

perl Group TitleBest ResponseYou've already chosen the best response.0
whats solution
 2 years ago

badreferences Group TitleBest ResponseYou've already chosen the best response.1
I'll post it when I can pick it up, Sir, it's not in my possession right now.
 2 years ago

perl Group TitleBest ResponseYou've already chosen the best response.0
dw:1348817984611:dw
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.0
see if this is right or not http://openstudy.com/study#/updates/50651902e4b08d185211d536
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.0
i proved that\[f_1(x)=x+x^2\]and\[f_{n+1}(x)=x(f_n(x)+f_n^'(x))\]
 2 years ago

badreferences Group TitleBest ResponseYou've already chosen the best response.1
Full solution. I can't seem to attach the .ps file so I did a screencap with ghostview,
 2 years ago
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