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What is the sum of the coefficients in the expansion of (1 + x)n ?

What is the sum of the coefficients in the expansion of (1 + x)n ? Correct Answer 2<sup>n</sup>

Concept:

(1 + x)n = nC0 x0+ nC1 x1 + nC2 x2 + …. + nCn xn

Calculation:

(1 + x)n = nC0 x0+ nC1 x1 + nC2 x2 + …. + nCn xn

Put x = 1, we get

⇒ (1 + 1)n = nC0 10+ nC1 11 + nC2 12 + …. + nCn 1n

⇒ nC0 10+ nC1 11 + nC2 12 + …. + nCn 1n = 2n

∴ nC0 + nC1 + nC2 + …. + nCn = 2n

Hence sum of the coefficients in the expansion of (1 + x)n is 2n

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