The sum of coefficients of integral power of | vedclass

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Question

${\left( {1 - 2\sqrt x } \right)^{50}} = {^{50}}{c_0} - {^{50}}{c_1}{\left( {2\sqrt x } \right)^1}$${\left( {1 - 2\sqrt x } \right)^{50}} = {^{50}}{c_

Vedclass · Accepted Answer

$\;\frac{1}{2}\left( {{3^{50}} + 1} \right)$

Vedclass · Answer

${\left( {1 - 2\sqrt x } \right)^{50}} = {^{50}}{c_0} - {^{50}}{c_1}{\left( {2\sqrt x } \right)^1}$${\left( {1 - 2\sqrt x } \right)^{50}} = {^{50}}{c_0} - {^{50}}{c_1}{\left( {2\sqrt x } \right)^1}$$ + {^{50}}{c_4}\left( {2\sqrt x } \right)4.....$

$s = {^{50}}{c_0} + {^{50}}{c_2} \cdot {2^2} + {^{50}}{c_4}{\left( 2 \right)^4} + .... + {^{50}}c_{502}^{50}$

${\left( {1 + x} \right)^{50}} = 1 + {^{50}}{C_1}{x^1} + {^{50}}{c_2}{x^2} + ...$

$x = 2, - 2$

${\left( {1 + 2} \right)^{50}} = 1 + {^{50}}{c_1}\left( 2 \right) + {^{50}}{c_2}{\left( 2 \right)^2} + ..$

${\left( {1 - 2} \right)^{50}} = 1 - {^{50}}{c_1}\left( 2 \right) + $${^{50}}{c_2}{\left( 2 \right)^2} - {^{50}}{C_3}{\left( 2 \right)^3} + .....$

${3^{50}} + 1$$ = 2\left[ {{^{50}}{C_0} + {^{50}}{c_2}{{\left( 2 \right)}^2} + {^{50}}{c_4}{{\left( 2 \right)}^4} + ..} \right]$

$\frac{{{3^{50}} + 1}}{2}$$ = {^{50}}{C_0} + {^{50}}{c_2}\left( 2 \right) + {^{50}}{c_4}{\left( 2 \right)^4} + ...$

The sum of coefficients of integral power of $x$ in the binomial expansion ${\left( {1 - 2\sqrt x } \right)^{50}}$ is :

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