Question Number 24542 by Tinkutara last updated on 20/Nov/17
![Prove that coefficient of x^n in ((a+bx+cx^2 )/e^x ) is (((−1)^n )/(n!))[cn^2 −(b+c)n+a]](Q24542.png)
$${Prove}\:{that}\:{coefficient}\:{of}\:{x}^{{n}} \:{in} \\ $$$$\frac{{a}+{bx}+{cx}^{\mathrm{2}} }{{e}^{{x}} }\:{is}\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}!}\left[{cn}^{\mathrm{2}} −\left({b}+{c}\right){n}+{a}\right] \\ $$
Commented by Tinkutara last updated on 20/Nov/17
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{very}\:\mathrm{much}\:\mathrm{Sir}! \\ $$
Commented by prakash jain last updated on 20/Nov/17
$$\frac{\mathrm{1}}{{e}^{{x}} }={e}^{−{x}} =\mathrm{1}−{x}+\frac{{x}^{\mathrm{2}} }{\mathrm{2}!}+−... \\ $$$$\mathrm{multiply}\:\mathrm{to}\:\mathrm{get}\:\mathrm{the}\:\mathrm{required}\:\mathrm{answer} \\ $$