Question

Binomial Theorem :- Find the value of x to the power n in the expansion of the following mentioned in the attachment


CONTENT QUALITY
NO SPAMMING​

Answer 1

Answer:

consider i as factorial

${e}^{ - x} = \sum {( - 1)}^{k} \frac{ { {x}^{k} }} {k \: i}$

so answer will be

a× x^n coefficient + b × x^(n-1) coefficient +c×x^(n-2) coefficient in e^(-x)

$a( \frac{ {( - 1)}^{n} }{n \: i}) + b(\frac{ {( - 1)}^{n - 1} }{(n - 1)\: i}) + c(\frac{ {( - 1)}^{n - 2} }{(n - 2)\: i}) \\ = (\frac{ {( - 1)}^{n} }{n \: i})(a - bn + n(n - 1)c) \\ = (\frac{ {( - 1)}^{n} }{n \: i})(c {n}^{2} - (b + n)c + a)$

Answer 2

Answer:

A is correct option

Step-by-step explanation:

formulee used--->

-------------------------------------

x x^2 x^3

1.e^-x=1- ----- + ------ - ------- +..............

1! 2! 3!

2. n! = n (n-1)!