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# The sum of coefficients of odd powers of $x$ in the expansion $(1+x)^{50}$ is ?

$\begin{array}{1 1} 0 \\ 2^{49} \\ 2^{50} \\ 2^{51} \end{array}$

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## 1 Answer

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$(1+x)^n=^nC_0+^nC_1x+^nC_2x^2+..........^nC_nx^n$.....(i)
$(1-x)^n=^nC_0-^nC_1x+^nC_2x^2-..........^nC_nx^n$....(ii)
$=(^nC_0+^nC_2x^2+^nC_4+......)$ - $(^nC_1x+^nC_3x^3+^nC_5x^5+........)$
Take $x=1,\:\:and\:\:n=50$ in $(i)$
$2^{50}=^nC_0+^nC_1+^nC_2+.........^nC_n$