The coefficient of x^7 in the expression (1+x)^(10)+x(1+x)^9 +x^2(1+x)^8+...+x^(10) is: A)420 B)330 C)210 D)120

Mia Pitts

Mia Pitts

Answered question

2023-02-26

The coefficient of x 7 in the expression ( 1 + x ) 10 + x ( 1 + x ) 9 + x 2 ( 1 + x ) 8 + . . . + x 10 is :
A)420
B)330
C)210
D)120

Answer & Explanation

Darien Jennings

Darien Jennings

Beginner2023-02-27Added 9 answers

The right decision is B 330
( 1 + x ) 10 + x ( 1 + x ) 9 + x 2 ( 1 + x ) 8 + . . . + x 10
Applying sum of terms of a G.P., we obtain
( 1 + x ) 10 + x ( 1 + x ) 9 + x 2 ( 1 + x ) 8 + . . . + x 10
= ( 1 + x ) 10 [ 1 ( x 1 + x ) 11 ] ( 1 x 1 + x )
= ( 1 + x ) 11 x 11
Coefficient of x 7 is 11 C 7 = 330

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