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Question Number 23700 by Tinkutara last updated on 04/Nov/17

If {(1 - x^{3})}^{n} = \underset{r = 0}{\sum^{n}} a_{r} x^{r} {(1 - x)}^{3 n - 2 r}, then

the value of a_{r}, where n \in N is

(1)^{n} C_{r} \cdot 3^{r}

(2)^{n} C_{3 r}

(3)^{n} C_{r - 1} 2^{r - 1}

(4)^{n} C_{r} 2^{r}

Commented by ajfour last updated on 04/Nov/17

I f n = 1

1 - x^{3} = a_{0} {(1 - x)}^{3} + a_{1} x (1 - x)

\Rightarrow a_{0} = 1 a n d a_{1} = 3

i f w e c h e c k o p t i o n s w i t h n = 1

(1) g i v e s a_{0} = 1, a_{1} = 3

(2) a_{0} = 1, a_{1} =!

(3) a_{0} =!, a_{1} = 1

(4) a_{0} = 1, a_{1} = 2

S o o n l y o p t i o n (1) q u a l i f i e s . .

Commented by Tinkutara last updated on 05/Nov/17

Not any proof ?

Commented by ajfour last updated on 05/Nov/17

i w i l l t r y . .

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