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

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

Concept:

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

Calculations:

We know that (1 + x)n = nC0 + nC1 x + nC2 x2 +...+ nCn xn

To find the sum of all the coefficients in the expansion of (1 + x)n , put x = 1

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

⇒(2)n = nC0 + nC1 + nC2 +...+ nCn 

⇒ nC0 + nC1 + nC2 +...+ nCn= 2n

Hence, the sum of all the coefficients in the expansion of (1 + x)n = 2n

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