f(x) = (x − 1)(x − 2)(x − 3)...(x − 50) Find coefficient of x^(49)


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Question Number 29777 by Joel578 last updated on 12/Feb/18

$f (x) = (x - 1) (x - 2) (x - 3) . . . (x - 50)$ $Find coefficient of x^{49}$
Commented by mrW2 last updated on 12/Feb/18

$s e e Q 29805$
Commented by 803jaideep@gmail.com last updated on 12/Feb/18

$i guess yesterday ques was upto x - 60$
Commented by Joel578 last updated on 12/Feb/18

$It was my mistake . It should be (x - 50)$
Commented by mrW2 last updated on 12/Feb/18

$t h e m o r e c h a l l e n g i n g q u e s t i o n i s :$ $f i n d t h e c o e f f i c i e n t o f x^{k} w i t h 0 ⩽ k ⩽ 50 .$
Commented by 803jaideep@gmail.com last updated on 12/Feb/18

$thn plz take an example and make$ $us learn about some mid value sir$ $. . like 30 or 25$
	Answered by puneet1789 last updated on 12/Feb/18

	Commented by Joel578 last updated on 12/Feb/18

	$t h a n k y o u v e r y m u c h$
	Answered by mrW2 last updated on 13/Feb/18

	$s e e Q 29805$ $h e r e n = 50$ $a_{k} = - k, 1 ⩽ k ⩽ 50$ $P = a_{1} a_{2} . . . a_{50} = 50!$ $c o e f f i c i e n t o f x^{49} :$ $C_{49} = \underset{1}{\sum^{50}} a_{i} = - (1 + 2 + . . . + 50) = - \frac{50 \times 51}{2} = - 1275$ $c o e f f i c i e n t o f x^{30} :$ $C_{30} = \frac{P}{1 \times 2 \times 3 . . . 30} + \frac{P}{1 \times 3 \times 4 . . . 31} + \frac{P}{1 \times 4 \times 5 . . . 32} + . . . + \frac{P}{1 \times 22 \times 23 . . . 50}$ $+ \frac{P}{2 \times 3 \times 4 . . . 31} + \frac{P}{2 \times 4 \times 5 . . . 32} + \frac{P}{2 \times 5 \times 6 . . . 33} + . . . + \frac{P}{2 \times 22 \times 23 . . . 50}$ $+ \frac{P}{3 \times 4 \times 5 . . . 32} + \frac{P}{3 \times 5 \times 6 . . . 33} + \frac{P}{3 \times 6 \times 7 . . . 34} + . . . + \frac{P}{3 \times 22 \times 23 . . . 50}$ $. . . .$ $+ \frac{P}{20 \times 21 \times 22 . . . 49} + \frac{P}{20 \times 22 \times 23 . . . 50}$ $+ \frac{P}{21 \times 22 \times 23 . . . 50}$ $= . . . . .$
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