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Sum of Coefficients of All Terms

If the sum of...

Question

If the sum of the coefficients in the expansion of ${(1 - 3 x + 10 x^{2})}^{n}$ is $a$ and if the sum of the coefficients in the expansion of ${(1 + x^{2})}^{n}$ is $b$ , then

a = 3 b

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a = b^{3}

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b = a^{3}

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3 a = b

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Solution

The correct option is B $a = b^{3}$
We have, $a =$ sum of the coefficients in the expansion of ${(1 - 3 x + 10 x^{2})}^{n} = (1 - 3 + 10)^{n} = (8)^{n} = (2)^{3 n}$
(by putting $x = 1$ )
Now, $b =$ sum of the coefficients in the expansion of ${(1 + x^{2})}^{n}$

$= (1 + 1)^{n} = 2^{n} . Clearly, a = b^{3}$

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Sum of Coefficients of All Terms

Standard XII Mathematics

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