The coefficient of $x^{6}$ in ${(1 + x)^{6} + (1 + x)^{7} + . . . . . + (1 + x)^{15}}$ is

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Solution

The correct option is A
$E x p r e s s i o n = \frac{(1 + x)^{6} {1 - (1 + x)^{10}}}{1 - (1 + x)}; s u m o f 10 t e r m o f G P = \frac{(1 + x)^{16} - (1 + x)^{6}}{x} ∴ T h e r e q u i r e d c o e f f i c i e n t = t h e c o e f f i c i e n t o f x^{7} i s {(1 + x)^{16} - (1 + x)^{6}} =^{16} C_{7} =^{16} C_{9}$

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Similar questions

Q. The coefficient of

x^{6}

[(1 + x)^{6} + (1 + x)^{7} + . . . . + (1 + x)^{15}]

Q. The coefficient of

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(1 + x)^{6}

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Q. Coefficient of

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Find the coefficient of $x^{15}$ in $(x^{3} + x^{6} + x^{9} + . . . . . . . . . . .) (x^{2} + x^{4} + x^{6} + . . . . . . . . . . .) (x + x^{2} + x^{3} + . . . . . . . . . .)$

Coefficient of $x^{6}$ in $((1 + x) (1 + x^{2})^{2} (1 + x^{3})^{3} . . . . (1 + x^{n})^{n})$ is

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The coefficient of x6 in {(1+x)6+(1+x)7+.....+(1+x)15}is

The correct option is A Expression=(1+x)6{1−(1+x)10}1−(1+x);sum of 10 term of GP=(1+x)16−(1+x)6x∴The required coefficient=the coefficient of x7 is {(1+x)16−(1+x)6}=16C7=16C9

The coefficient of $x^{6}$ in ${(1 + x)^{6} + (1 + x)^{7} + . . . . . + (1 + x)^{15}}$ is