Prove-that-coefficient-of-x-n-in-a-bx-cx-2-e-x-is-1-n-n-cn-2-b-c-n-a-

Question Number 24542 by Tinkutara last updated on 20/Nov/17

P r o v e t h a t c o e f f i c i e n t o f x^{n} i n

\frac{a + b x + {c x}^{2}}{e^{x}} i s \frac{{(- 1)}^{n}}{n!} [{c n}^{2} - (b + c) n + a]

Commented by Tinkutara last updated on 20/Nov/17

Thank you very much Sir!

Commented by prakash jain last updated on 20/Nov/17

\frac{1}{e^{x}} = e^{- x} = 1 - x + \frac{x^{2}}{2!} + - \dots

multiply to get the required answer