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  • In the expansion of  <img alt="(1+x)^{50}" src="https://entrancecorner.oncodecogs.com/gif.latex?%281&plus;x%2

In the expansion of  (1+x)^{50}, let S be the sum of coefficients of odd power of x, then  S is

 

Option: 1

0


Option: 2

2^{49}


Option: 3

2^{50}


Option: 4

2^{51}


Answers (1)

best_answer

(1+\mathrm{x})^{50}=1+{ }^{50} \mathrm{C}_1 \mathrm{x}+{ }^{50} \mathrm{C}_2 \mathrm{x}^2+{ }^{50} \mathrm{C}_3 \mathrm{x}^3+\ldots \ldots+{ }^{50} \mathrm{C}_{49} \mathrm{x}^{49}+{ }^{50} \mathrm{C}_{50} \mathrm{x}^5^0

Sum of coefficients of odd powers of x

{ }^{50} \mathrm{C}_1+{ }^{50} \mathrm{C}_3+\ldots \ldots .+{ }^{50} \mathrm{C}_{49}=2^{50-1}=2^{49}.

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Gaurav

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