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

Question

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

Darien Jennings · Accepted Answer

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

The coefficient of x 7 in the expression ( 1 + x ) 10 +...

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