Question

here is the another interesting problem.
find the coefficient of x^9 in the expansion of
$(1 + x)(1 + {x)}^{2} (1 + {x}^{3} )...(1 + {x}^{100} )$
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Answer 1

Step-by-step explanation:

Answer:

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Step-by-step explanation:

hope it help you.

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Answer 2

Step-by-step explanation:

Given :-

(1+x)(1+x²)(1+x³)...(1+x¹⁰⁰)

To find :-

Find the coefficient of x⁹ ?

Solution :-

Given that

(1+x)(1+x²)(1+x³)...(1+x¹⁰⁰)

required coefficient = the coefficient of x⁹

x⁹ is formed by these ways

1) 1×x⁹ = x⁹

2) x¹×x⁸ = x⁹

3) x²×x⁷ = x⁹

4) x³×x⁶ = x⁹

5) x⁴×x⁵ = x⁹

6) x¹×x²×x⁶ = x⁹

7) x¹×x³×x⁵ = x⁹

8) x²×x³×x⁴ = x⁹

total number of ways to get x⁹ = 8

The coefficient of x⁹ = 8

Since,

Coefficient of x⁹

= (1×x⁹)+(x¹×x⁸)+(x²×x⁷)+(x³×x⁶)+(x⁴×x⁵)+(x¹×x²×x⁶) +(x¹×x³×x⁵)+(x²×x³×x⁴)

= (1+1+1+1+1+1+1+1)x⁹

= 8x⁹

Answer:-

The coefficient of x⁹ = 8