Find-the-coefficient-of-in-the-expansion-of-1-x-1-x-2-1-x-3-1-x-n-

Question Number 8168 by aungnaingsoe last updated on 02/Oct/16

F i n d t h e c o e f f i c i e n t o f i n t h e e x p a n s i o n o f

(1 + x) (1 + x^{2}) (1 + x^{3}) \dots (1 + x^{n}) .

Commented by Rasheed Soomro last updated on 02/Oct/16

c o e f f i c i e n t o f w h a t ?

Commented by lepan last updated on 02/Oct/16

x^{9}

Commented by 123456 last updated on 03/Oct/16

[\begin{matrix} 0 \\ 1 \end{matrix}] [\begin{matrix} 0 \\ 2 \end{matrix}] [\begin{matrix} 0 \\ 3 \end{matrix}] \dots [\begin{matrix} 0 \\ n \end{matrix}]

p_{n} (x) = \underset{i = 1}{\prod^{n}} (1 + x^{i})

1 ⩽ n ⩽ 3

G [p_{n}] ⩽ 6 \Rightarrow C_{9} = 0

n ⩾ 4

G [p_{n}] ⩾ 9

- - - - - - - - - - -

2

18, 27, 36, 45 : 4

3

∙ 1

126, 135 : 2

∙ 2

234 : 1

- - - - - - - - -

n = 4 \Rightarrow C_{9} = 1

n = 5 \Rightarrow C_{9} = 3

n = 6 \Rightarrow C_{9} = 5

n = 7 \Rightarrow C_{9} = 6

n ⩾ 8 \Rightarrow C_{9} = 7

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