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The sum of coefficients of  even  powers of x  in the  expansion of \left(x+\frac{1}{x}\right)^{11}  is

Option: 1

11 \times{ }^{11} \mathrm{C}_5


Option: 2

\frac{11}{2} \times{ }^{11} \mathrm{C}_6


Option: 3

11\left({ }^{11} \mathrm{C}_5+{ }^{11} \mathrm{C}_6\right)


Option: 4

0


Answers (1)

best_answer

(r+1)^{\text {th }} \text { term }={ }^{11} C_r(x)^{11-r} \cdot x^{-r}

={ }^{11} C_r \cdot x^{11-2 r}

Even power of x exists only if 11 − 2 r = an even number not possible 

Sum of coefficient = 0

 

Posted by

manish painkra

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