f-x-x-1-x-2-x-3-x-50-Find-coefficient-of-x-49-

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

f (x) = (x - 1) (x - 2) (x - 3) \dots (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} \dots 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 + \dots + 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 \dots 30} + \frac{P}{1 \times 3 \times 4 \dots 31} + \frac{P}{1 \times 4 \times 5 \dots 32} + \dots + \frac{P}{1 \times 22 \times 23 \dots 50}

+ \frac{P}{2 \times 3 \times 4 \dots 31} + \frac{P}{2 \times 4 \times 5 \dots 32} + \frac{P}{2 \times 5 \times 6 \dots 33} + \dots + \frac{P}{2 \times 22 \times 23 \dots 50}

+ \frac{P}{3 \times 4 \times 5 \dots 32} + \frac{P}{3 \times 5 \times 6 \dots 33} + \frac{P}{3 \times 6 \times 7 \dots 34} + \dots + \frac{P}{3 \times 22 \times 23 \dots 50}

\dots .

+ \frac{P}{20 \times 21 \times 22 \dots 49} + \frac{P}{20 \times 22 \times 23 \dots 50}

+ \frac{P}{21 \times 22 \times 23 \dots 50}

= \dots . .

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